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Surface Color Perception under Different

Illuminants and Surface Collections

Inaugural-Dissertation zur Erlangung der Doktorwurde

der Philosophischen Fakultat II

(Psychologie, Padagogik und Sportwissenschaft)

der Universitat Regensburg

vorgelegt von

Claus Arnold

aus Regensburg

Regensburg 2009

Erstgutachter: Prof. Dr. Karl-Heinz Bauml

Zweitgutachter: Prof. Dr. Mark Greenlee

i

”We do not see things as they are; we see things as we are.”

- Talmud

Contents

1 Introduction 1

1.1 Color constancy as a perceptual constancy . . . . . . . . . . . 3

1.2 Open issues of color constancy . . . . . . . . . . . . . . . . . . 7

1.3 Chapter overview . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Foundations of color constancy 13

2.1 From light to color . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Receptor site . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.2 Opponent site . . . . . . . . . . . . . . . . . . . . . . . 17

2.1.3 Cortex site . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 The color constancy problem . . . . . . . . . . . . . . . . . . . 21

2.3 Sensory, perceptual, and cognitive processes of color constancy 24

2.3.1 Sensory processes . . . . . . . . . . . . . . . . . . . . . 25

2.3.2 Perceptual processes . . . . . . . . . . . . . . . . . . . 28

2.3.3 Cognitive processes . . . . . . . . . . . . . . . . . . . . 31

2.4 Measuring color constancy . . . . . . . . . . . . . . . . . . . . 31

ii

CONTENTS iii

2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3 Color constancy under different illuminants and surface col-

lections 36

3.1 Illuminants and surfaces in our environment . . . . . . . . . . 36

3.2 Color constancy under different illuminants . . . . . . . . . . . 41

3.3 Color constancy under different surface collections . . . . . . . 43

3.4 Goals of the study . . . . . . . . . . . . . . . . . . . . . . . . 45

4 General methods 47

4.1 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

4.2 Experimental illuminants and surfaces . . . . . . . . . . . . . 48

4.3 General procedure . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5 Experiments 55

5.1 Experiment 1: The role of luminance in illuminant changes . . 55

5.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.1.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.2 Experiment 2: The role of color direction in illuminant changes 66

5.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 82

CONTENTS iv

5.3 Experiment 3: The role of color direction under various signal–

to–noise ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.4 Experiment 4: The role of surface collection in illuminant

changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.4.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 105

6 General Discussion 108

Bibliography 118

Appendix A 129

Acknowledgments 134

Chapter 1

Introduction

It is important for our daily life that we are able to visually identify and

discriminate objects. Our ancestors could not even have survived without the

ability to identify dangerous animals or discriminate ripe from non–ripe fruit.

Objects have several attributes by which we can identify and discriminate

them. Important attributes are size, shape, and color.

Unfortunately, environmental conditions change every now and then and

affect these attributes. Consider a table as an example of an object (Figure

1.1). If we alter the distance between us and the table, the apparent size of

the table changes. If we rotate the table by some angle, the apparent shape

of the table changes. We are consciously aware that these changes occur, and

that the perceived picture of the object changes. However, we do not interpret

these changes as though the table as an object has changed in size or shape.

In fact, we perceive the table as an object roughly constant in size and shape.

These two features of our visual system are called size constancy and shape

constancy, respectively (see Wandell, 1995). They are examples of perceptual

constancies that help us compensate for changes in our environment to keep

1

CHAPTER 1. INTRODUCTION 2

Figure 1.1: Size constancy (top row) and shape constancy (bottom row) exempli-

fied by a table as a sample object. The object gets moved from an initial position

(left column) to a new position (middle column). This transformation modulates

apparent size and shape of the object. That becomes particularly obvious when

depicting the objects in isolation (right column). Despite this, the table as an

object within the scenes is perceived roughly constant in size and shape.


certain properties of objects at least roughly constant.

As we see in this example, for each attribute a clear distinction has to

be made. First, apparent size and apparent shape correspond roughly to the

retinal image of the object we look at and seems to be mediated by lower

sensory processes of our visual system. Apparent size and apparent shape

vary when changes in viewing distance to the object or changes in orientation

of the object occur. Second, object size and object shape are mediated

by higher, perceptual processes in the visual system. These processes bind

the visual features of size and shape more to the object and use contextual

attributes, like viewing distance and viewing angle, to generate an integral

representation of the object (Rock & Linnett, 1993). Object size and object

shape do not vary a lot when the context changes, thus reflecting perceptual

constancies. It is important to note that we are aware of this distinction and

that we can consciously switch between apparent and object code. Figure

1.1 depicts the above example of size and shape constancy and shows the

distinction between apparent and object code.

1.1 Color constancy as a perceptual constancy

Another important attribute of objects is color. This attribute underlies

changes in our environment as well. Consider a situation in which our table

is illuminated by diffuse daylight through a window. While we are work-

ing on that table for some time the incident daylight changes rather slowly

depending on daytime and weather conditions (Figure 1.2a). Despite these

changes the color of the table surface remains roughly the same. Due to its

slowness we are not aware of the illuminant change. The visual system is able

to adjust to slow illuminant changes, discount the illuminant effect, and thus


hold the color sensation, i. e. the apparent color, of the table roughly con-

stant. Such adaptational mechanisms are considered to be fairly low–level,

sensory processes (Kaiser & Boynton, 1996). We can describe apparent color

in terms of hue, saturation, and brightness of the reflected light that meets

the eye. These three attributes of color are helpful for us to give a unique

description of a particular color sensation.

In another situation color can also be described as more related to the

surface properties of the object itself rather than in terms of hue, saturation,

and brightness of the apparent color of the reflected light. Consider our

table located in a room illuminated by an ambient light. If we push the table

against a window, part of the table surface may be locally illuminated by

incident sunlight and the table as a whole is globally illuminated by ambient

room light (Figure 1.2b). So there are two differently illuminated areas on

the table surface that have distinct apparent colors. In contrast to the first

situation, where illumination changed temporally slowly, the visual system

has to deal with a rather abrupt spatial illuminant change. We are aware

that this spatial illuminant change occurs and that rather different apparent

colors are present within the scene. However, we do not interpret this change

as though the table as an object has changed in color. In fact, we perceive

the table as an object that has a roughly constant object color. Apparent

color code as a description of the table surface color is of limited use in this

type of situation where more than one light source is present since adaptation

of the visual system is time-consuming and may take more than a minute (e.

g. Fairchild & Reniff, 1994).

A third situation can be identified in which object color plays an impor-

tant role to achieve constant color percepts. Consider our table located in a

room diffusely illuminated by daylight through a window. When we switch


on a tungsten bulb or a luminescent tube the overall illumination on the table

changes abruptly (Figure 1.2c). Due to this, the apparent color of the table

most likely changes as well. However, the object color of the table remains

roughly the same. Our visual system has the ability to discriminate whether

such a rapid temporal change in apparent color was due to an illuminant

change or due to a change in object surface. In this situation, apparent color

code is not a sufficiently useful description of the table color as well since illu-

mination changes too fast for the visual system to use low–level adaptational

mechanisms to achieve a constant color percept.

For each of the three described situations either apparent color or object

color is the appropriate object description to achieve constant color percepts.

Apparent color is mediated by low–level, sensory mechanisms, in which adap-

tation plays an important role (von Kries, 1905). In contrast, object color is

mediated by higher–order, perceptual mechanisms (Helmholtz, 1866). These

mechanisms relate color to the object and use contextual cues, such as illumi-

nants and other objects in the scene, to generate an integral representation

of the object. Often we are aware of the distinction between apparent color

and object color and may even be able to switch consciously between the

codes.

Three situations could be identified where one or both of the two descrip-

tions of color help to achieve constant color percepts. In the first situation,

illumination changes rather slowly over time. The visual system is given

enough time to adapt to these changes. Apparent color serves as appropriate

descriptions for a constant color. Since illumination changes rather slowly

over time this ability of the visual system to adjust to such a change is called

successive color constancy.


a)

b)

c)

>2min

<1sec

Figure 1.2: The three color constancy situations. a) The room is diffusely illumi-

nated by daylight through the window. The illuminant changes rather slowly over

time (successive color constancy). b) The table is globally illuminated by ambi-

ent room light and partly by direct sunlight through the window. The illuminant

changes spatially yielding two different illuminants within the scene (simultaneous

color constancy). c) The room is illuminated by daylight through the window.

Then a tungsten bulb is switched on. The illuminant changes rapidly over time.


In the second situation, more than one illuminant is present within a

scene, so illumination changes spatially. When a scene is illuminated by at

least two illuminants apparent color processes do not provide an appropriate

description of the colors since the visual system is not given enough time to

adapt to either of the illuminants appropriately. Higher–order, perceptual

object color processes compensate for this lack and give a roughly correct

description of the color. It is important, however, that the observer shifts his

view back and fourth between the differently illuminated parts of the scene

to avoid strong adaptation to any of the illuminants. In this type of situation

a scene is simultaneously illuminated by more than one light. Therefore, this

type of visual compensation for illuminant changes is called simultaneous

color constancy.

In the third situation the overall illumination changes rapidly over time.

This change of illuminant yields a change in apparent colors of the objects

located in this room. As above, apparent color processes are too slow to com-

pensate for such a rapid illuminant change. However, perceptual mechanisms

step in and help achieving an appropriate color description.

1.2 Open issues of color constancy

Previous research focussed on investigating visual adjustment to changing

illumination using successive and simultaneous color constancy paradigms

(e. g. Brainard & Wandell, 1992; Arend & Reeves, 1986). The goals of

these studies were mainly to examine the basic characteristics of the visual

adjustment processes. Some basic principles were found. A first principle

states that visual adjustment can be described as an appropriate scaling of

the responses of the three receptor classes to the changing illumination (see


chapter 2.1 below), a principle called receptor scaling or von Kries principle

(von Kries, 1905). The second principle states that the scalings of the re-

ceptor responses vary linearly with an illuminant change, a principle called

illuminant linearity. The principles were confirmed under a variety of illu-

minants and surface sets of which the scenes were constructed since it is

important that color constancy holds under common illuminant changes and

in a variety of scenes. Additionally, there are some studies which focus on

the issue to which extent color constancy works under particular illuminants

or surface collections.

There is also some research which deals with color constancy in situations

in which illuminant changes occur temporally abrupt (e. g. Craven & Foster,

1992). The methods used are always discrimination paradigms of some sort.

Observers are presented two images in rapid succession. Between the images

either an illuminant change occurs or the surfaces of which the images are

made up are changed. Observers are asked to judge whether the change

between the images was due to an illuminant change or due to a change

in surfaces. It was shown that observers are able to make these judgments

reliably and effortlessly. However, for this type of situation not much is

known about how constant our visual system is under different illuminants

or surface collections. For a better understanding of color constancy under

rapidly changing illuminants this gap is supposed to be filled. Additionally,

a comparison of the result patterns for this paradigm and successive and

simultaneous color constancy paradigms would provide a better insight to

which extent the paradigms are related with respect to which results they

produce.

Existing theories of color constancy frequently involve the above men-

tioned principles of receptor scaling and illuminant linearity. Since the latter


principle tells us about the dependency of visual adjustment on the illumi-

nant change, illuminant linearity might be challenged when the degree of

color constancy varies drastically with illuminant direction or surface collec-

tion. It is not clear by now which impact such results would have on existing

theories of color constancy.

The aim of the present work is to give some answers to the issues de-

scribed above. A series of experiments is reported in which color constancy

under various rapid illuminant changes and surfaces collections is investi-

gated. The results of the experiments are supposed to contribute to a better

understanding of color constancy.

1.3 Chapter overview

The remainder of this work is structured as follows. Chapter 2 deals with

the foundations of color constancy. In the first section, it is described how

the light incident at the eye is composed and how this light signal is encoded

at different sites within the visual system to generate a color percept. In

the second section, it is explained what the fundamental problem of color

constancy is like. In the third section, sensory, perceptual, and cognitive

processes are described supposed to play a role in mediating color constancy.

Chapter 3 prepares the empirical part of this work. It describes which

illuminants and surfaces we encounter in our everyday environment. After

that it reclaims previous studies which deal with the role of illuminant color

direction and surface collection for color constancy. The goals of this work

are pointed out.

Chapter 4 describes the general methods applied for all the experiments in


this work. Additional methodological aspects are described in the ”Methods”

sections of the respective experiments. In all experiments, the operational

paradigm derived from Craven & Foster (1992) is used. A brief summary of

the setups used in the particular experiments is also provided.

In chapter 5, four experiments are described which deal with surface color

perception under different illuminants and surface collections. In Experiment

1, I investigate which role a change in luminance can play when the illumina-

tion on a scene changes. In previous color constancy experiments, the focus

was on the role of chromaticity in illuminant changes while luminance of

the illuminant was either held constant or was not controlled at all. In this

experiment, conditions where illuminant changes were either isoluminant,

or isochromatic, or where both chromaticity and luminance changed were

designed. The results of the experiment show that the effect of luminance

changes on color constancy is small.

Experiment 2 deals with the role of color direction in illuminant changes.

Previous studies on this topic mainly focussed on illuminant changes along

the daylight axis. However, since illuminations on a scene are mostly influ-

enced by non–daylight illumination that deviates from the daylight axis it is

important to investigate color constancy under illuminant changes along an

orthogonal red–green axis as well. Results of this experiment show high color

constancy under illumination changes along the green and blue semi–axes,

medium constancy along the yellow semi–axis, and rather low constancy un-

der changes along the red semi–axis. In a second step I tried to investigate

how color constancy in further illuminant directions fit in the color con-

stancy pattern obtained. Four additional test illuminants were introduced.

Results show that color constancy performance in all eight illuminant direc-

tions yields a smooth pattern with highest constancy in greenish and bluish


directions, medium constancy in yellowish directions, and lowest constancy

in reddish directions. In Experiment 3, I investigate if the obtained pattern

of color constancy values would be stable under variations of signal–to–noise

ratios. By increasing and reducing noise in two separated conditions task

difficulty is aggravated and facilitated, respectively. The results show that

the basic shape of the pattern remains largely constant across conditions.

Experiment 4 deals with color constancy under variation of objects within

a scene. It is investigated whether the degree of color constancy is constant

or differs under changes in surface collections. Surface sets which on average

appear blue, yellow, red, or green, when viewed under a neutral illuminant

together with the combined set which, on average, is neutral are used in this

experiment. A red and a blue illuminant are also used. Observers’ task is

again to discriminate illuminant changes from surface changes in the scenes.

Results show high color constancy with green and blue surface collections and

rather low constancy with the red collection. This pattern is rather similar

under the red and blue illuminants.

In chapter 6, a general discussion is provided. After an empirical sum-

mary, I draw conclusions from the experiments presented in this work in

order to give an answer to the questions raised prior in this work. There is

an influence of color direction to the degree of color constancy. There is also

an effect of surface collection which resembles the pattern obtained for the

respective illuminants. There seems to be little difference for the amount of

visual adjustment whether the resulting light incident at the eye stems from

the variation of illuminant colors or from the variation of surface collections.

The evolutionary approach might propose an explanation to the present re-

sults. The effect of individual differences and a comparison of the results

to the findings in successive and simultaneous situations are also discussed.


The general discussion closes with implications for further research.

Chapter 2

Foundations of color constancy

2.1 From light to color

The classic psychophysical experiment to investigate color vision is the color–

matching experiment. An observer looks at a bipartite field consisting of a

test side and a match side. The test side shows a particular color. The match

side shows a color that is an additive mixture of so–called primary lights,

which have independent spectral power distributions. The intensity of these

primaries can be independently manipulated by the observer. The task of

the observer is to adjust the intensities, i. e. the weights, of the primaries

to match the apparent color of the match field to the apparent color of the

test field. It can be shown that such a match can always be achieved with at

least three primary lights1. Considering the high–dimensional spectral power

1There is a restriction to this assertion, since not every light can be matched by an

additive mixture of three primary lights. For some lights, one of the primaries has to be

subtracted from the match side and added to the test side to achieve a match.

13

CHAPTER 2. FOUNDATIONS OF COLOR CONSTANCY 14

distribution of a light2, it is a remarkable feature of the human visual system

to get by with only three primaries. This feature is called trichromacy. Due

to this rigorous reduction of information, there are many lights which are

physically different but psychophysically indistinguishable.

In addition to trichromacy, the color matching experiment reveals two

other remarkable principles of color perception. First, when the intensity of

the light on the test side gets scaled, e. g. by doubling it, the observer also

doubles the intensity of the light on the match side to obtain a match. In

general, if a and b represent the lights on the test side and on the match side

and are perceptually equal, i. e. have the same color, then ka is perceptually

equal to kb. This law is called homogeneity. Second, when adding a second

light to the light on the test side to produce a color mixture, the observer

adjusts the light on the match side as if he added the same light which was

added to the test side. In general, if the lights a and b are perceptually

equal, then the additive mixture a + c is perceptually equal to the additive

mixture b + c. This law is called additivity. In other words, the symmetric

color matches are invariant to scaling and additive mixture.

The first to describe the three principles trichromacy, homogeneity, and

additivity was Grassmann (1853), which is why they are called Grassmann’s

laws. The important conclusion from these findings is that through homo-

geneity and additivity the sensation ’color’ can be numerically mapped into

a vector space. From trichromacy we also know that the dimensionality of

this space is three. However, there is no unique basis for this vector space.

Any set of three primaries — as long as they are linearly independent — may

2The dimensionality of a spectral power distribution depends on the sampling rate.

Sampled in 10 nm steps from 400 nm to 700 nm, as done for experiments in this work,

the dimensionality is 31.


be chosen in order to succeed in the color–matching experiment.

Based on the information of the color–matching experiment it has been

speculated that three classes of receptors in the visual system would suffice

to mediate color vision (Young, 1802; Helmholtz, 1866). However, where

exactly these receptors are sited, what their characteristics are, and how

the signals of the receptor responses are further processed, had yet to be

investigated.

2.1.1 Receptor site

The principle of trichromacy was first stated by Young (1802) and later re-

formulated by Helmholtz (1866). They hypothesized that there are three re-

ceptor classes in our retina, one that is mainly sensitive to short–wavelength

lights, one that is mainly sensitive to middle–wavelength lights, and one that

is mainly sensitive to long–wavelength lights. One approach to investigate

the characteristics of these receptors was to carry out further psychophys-

ical experiments. Important insights could be gained from color–matching

experiments with observers that lack one of the three receptor types. This

was done in a famous study by Smith & Pokorny (1975), who could thereby

estimate the sensitivity for each of the three receptor — or cone — classes as

a function of wavelength. Further estimates were done by Stockman, Sharpe,

& Fach (1999) and Stockman & Sharpe (2000). Figure 2.1 shows these so–

called Stockman–Sharpe estimates of the spectral sensitivity functions, which

are widely used in color science.

A second approach to investigate the spectral sensitivity functions of hu-

man receptor types is to measure the receptor response signals physiologi-

cally. This was first done in 1987, when three scientists published single–cell


400 500 600 700

1.0

0.5

0.0

wavelength [nm]

responsivity

1.0

0.5

0.0

responsivity

1.0

0.5

0.0

responsivity

L-cone

S-cone

M-cone

Figure 2.1: Estimated responsivities of the long–wavelength sensitive L–cone

class, the middle–wavelength sensitive M–cone class, and the short–wavelength

sensitive S–cone class (after Stockman & Sharpe, 2000).


conductions of the middle– and long–wavelength receptors of a human male

retina (Schnapf, Kraft, & Baylor, 1987; see also Brown & Wald, 1964, and

Dartnall, Bowmaker, & Mollon, 1983, for other measurement techniques).

Two outcomes of this study are notable. First, the measured spectral sen-

sitivity functions of human receptors are identical to those of receptors in

macaque monkeys’ retina within error of measurement (Baylor, Nunn, &

Schnapf, 1987). Second, they are almost completely identical with the psy-

chophysically obtained estimates by Smith & Pokorny (1975).

As shown, the spectral sensitivity functions of the color receptors in the

human retina were assessed by two different approaches leading to similar

results. This is important because the sensitivity functions provide a basis

for further investigation of color vision.

2.1.2 Opponent site

Hering (1878, 1905) observed that the colors red and green as well as blue

and yellow are perceptually linked as antagonistic pairs. He showed that

looking at a red surface induces a green afterimage and looking at a green

surface induces a red afterimage. Analogous results were obtained for the

blue–yellow pair. He also asked subjects to imagine a color that is a reddish

green or a yellowish blue. They could not perform the task although it was

easy for them to imagine a cross–combination of other hues like a greenish

yellow or a bluish red. These observations led Hering to his opponent colors

theory. He proposed three opponent mechanisms that respond complemen-

tary to light of different intensity or wavelength: a black/white mechanism,

a red/green mechanism, and a yellow/blue mechanism. Since Hering’s ob-

servations had been of phenomenological nature and could not be supported


by psychophysical or physiological correlates, his opponent colors theory was

widely unaccepted for a long time, as opposed to Helmholtz’ trichromacy

theory.

Half a century later, Jameson & Hurvich (1955) proposed their famous

hue cancellation paradigm, by which they were able to find psychophysi-

cal evidence for opponent color mechanisms. The goal of the study was to

measure the redness, greenness, blueness, and yellowness for every monochro-

matic light of the visible spectrum. For this purpose, Jameson and Hurvich

gave observers fixed red, green, blue, and yellow cancellation lights of single

wavelengths. They presented monochromatic test lights and asked observers

to cancel the redness out of the test light by adding the green cancellation

light. To cancel out the greenness of the light, observers were asked to add

the red cancellation light. The amount of added green cancellation light

was taken as a measure for the redness of the test light, and the amount of

added red cancellation light represented the greenness of the test light. Ana-

log procedures were applied for measuring blueness and yellowness of test

lights. Figure 2.2 shows responsivity functions of the opponent mechanisms

obtained by Jameson & Hurvich (1955) together with the responsivity func-

tion of the achromatic black/white system. The two zero–crossings of the

graph in the middle panel depict unique blue and unique yellow, respectively.

The zero–crossing of the graph in the bottom panel indicates unique green.

Unique red is non–spectral. These findings convinced the scientific commu-

nity to consider Hering’s theory. Since then, both trichromacy theory and

opponent colors theory stood side by side. Shortly after the psychophysical

findings, Svaetichin (1956) physiologically discovered opponent cells in the

retina of carps, which suggested the existence of a similar correlate in humans

and contributed to opponent colors theory from a physiological perspective.


responsivity

1.0

0.5

0.0

black/white

responsivity

1.0

0.0

-1.0400 500 600 700

wavelength [nm]

yellow/blue

responsivity

1.0

0.0

-1.0

red/green

Figure 2.2: Spectral responsivity functions of the achromatic black/white sys-

tem and the chromatic red/green and yellow/blue opponent color systems (after

Jameson & Hurvich, 1955).


Krauskopf, Williams, & Heeley (1982) psychophysically obtained cardinal

color directions for the three opponent color mechanisms. They found that

the L-, M-, and S-cone signals were roughly recoded into L-M, S-(L+M),

and L+M opponent color signals representing the red/green, yellow/blue,

and black/white channel, respectively. Although this simple transformation

of the cone signals was psychophysically confirmed, it was shown that the

neural correlates of the recoding are far more complex (Lee, 2004).

Yet we have a rather good understanding about color opponency from

further psychophysical studies (Gordon & Abramov, 1988; Abramov & Gor-

don, 1994; Bauml & Wandell, 1996; Poirson & Wandell, 1993). The basics

of the neural structure and wiring of receptor cells and opponent cells are

also known (Lee, 2004). However, since the end of the 19th century, a visual

cortex was postulated, where the signals from the retina converge and are

further processed (Verrey, 1888).

2.1.3 Cortex site

Verrey (1888) was the first to suggest the existence of a center for the chro-

matic sense in the human cortex (Zeki & Marini, 1998). Almost a century

later, Zeki (1973) could physiologically confirm color–specialized cortical cells

of rhesus monkeys. fMRI studies showed that there exists a visual pathway

leading through functionally separable cortical areas (Zeki & Marini, 1998).

This pathway starts at the area striata, also called V1, where retinal signals

converge. This area consists of small receptive fields that are highly sensitive

to changes in wavelength composition of light (Zeki, 1983). These V1 cells,

however, seem to be influenced by signals outside their receptive fields which

account for discounting the color of the background (Wachtler, Sejnowski,


& Albright, 2003; Hurlbert, 2003), thus being a first candidate for holding

colors constant by some color contrast mechanism. The signals are further

transferred to area V2, where different types of opponent color cells were

found (e. g. Derrington, Lennie & Krauskopf, 1983; de Valois & Jacobs,

1984). Area V4 consists of large receptive fields, which are activated when

looking at large multicolored scenes. This area is supposedly responsible for

global processing of images and is therefore a first candidate for mediating

color constancy (Bartels & Zeki, 2000). A recent study showed that the ma-

jority of V4 cells also shift their color–tuning functions appropriately when

illumination changes (Kusunoki, Moutoussis, & Zeki, 2006). However, V4

cells responsible for color vision and those responsible for spatial vision are

still hard to separate (Solomon & Lennie, 2007).

Despite these findings, the understanding of the functions of separate

areas in the visual cortex is far from complete. Investigating the cortical site

of color processing is a rather complex topic, and the description of the color

pathway still has substantial gaps. For good reviews of cortical processing of

color signals see Bartels & Zeki (2000) and Solomon & Lennie (2007).

2.2 The color constancy problem

In chapter 1, it was pointed out that the human visual system is capable

of holding object colors constant, despite variation in ambient illumination.

Successive color constancy refers to the finding that apparent colors remain

roughly constant when illumination changes rather slowly. Simultaneous

color constancy refers to the finding that object colors remain roughly con-

stant when illumination changes spatially in an abrupt way. A third type

of constancy refers to the finding that object colors remain roughly constant


when illumination changes temporally fast. However, when an illuminant

change takes place, photoreceptor responses, which are the first stage of color

coding, do not remain constant. Figure 2.3 depicts how the light incident

at the eye occurs. It is shown which receptor signals arise when a surface

is illuminated by two different lights. There are two factors mediating the

light reaching the eye: the illuminant and the surface. An illuminant may

be specified by its spectral power distribution. This is the radiant power

as a function of wavelength. Daylight illumination can vary drastically over

the day from white to bluish and yellowish (Judd, MacAdam, & Wyszecki,

1964). A surface may be specified by its reflectance function, which is a

physical attribute of the surface. It expresses the fraction of reflected light

as a function of wavelength. When an illuminant meets a surface, the re-

flected light may be expressed by the wavelength–by–wavelength product of

the spectral power distribution and the surface reflectance function. This

light stimulates the receptors in the retina, whose excitatory pattern ri can

be expressed by

ri =∑λ

E (λ)S (λ)Ri (λ)

where E is the spectral power distribution of the illuminant, S is the surface

reflectance function, and Ri are the sensitivity functions of the three receptor

classes i = L,M, S. It is shown in Figure 2.3 that a change in the spectral

power distribution of the illuminant leads to a different light incident at the

eye. As a result, the excitatory pattern of the receptors typically changes

with illumination. If our visual system solely relied on the information of the

receptor responses, colors would change drastically with illuminant changes.

It is therefore obvious that the visual system has to further process the

receptor signals to adjust to changes in illuminant and create robust color


400 500 600 700

400 500 600 700wavelength

wavelength

power

25

0

power

25

0

absorptionrate

1

0S LM

400 500 600 700


wavelength

power

25

0


fraction

1

0

power

25

0

1

0

absorptionrate

1

0S LM

400 500 600 700

responsivity

wavelength

illuminant

reflectance

illuminantx

reflectanceproduct

coneresponsivities

cone absorptionrates

Figure 2.3: Depiction of the color constancy problem. When a surface is illu-

minated by two different lights, different cone absorption rates might result. To

achieve a constant surface color, the visual system must compensate for this illu-

minant change.


signals. Investigating the nature of these processes is the subject of color

constancy research.

The next section gives a brief overview of the levels of the processes

supposed to be involved in mediating color constancy.

2.3 Sensory, perceptual, and cognitive pro-

cesses of color constancy

In section 2.1, the color pathway from the photoreceptors to the primary

visual cortex was described. Anywhere along this pathway, there have to be

one or more stages that process the light from objects viewed in a scene to a

constant color, with only small dependency on the surrounding illumination.

Physiologically, it is not entirely known where in the color pathway responsi-

ble processing stages are located. Psychophysically, the basic characteristics

of the visual adjustment process were already identified (e. g. Brainard &

Wandell, 1992; Bauml, 1999a). However, it is not known in detail how dif-

ferent processes work and how they interact with each other to achieve color

constancy in different everyday situations. It is common belief nowadays,

that there are several stages that mediate color constancy at different levels

of color processing (see Arend & Reeves, 1986; Hansen, Olkkonen, Walter, &

Gegenfurtner, 2006). This chapter deals with the question which processes

have already been identified that contribute to color constancy. Following

the color pathway, these processes can be classified into sensory, perceptual,

and cognitive categories.


2.3.1 Sensory processes

The retinal receptors are the stage where color processing begins, and their

responses provide the basis for every further operation on the signal. So,

the receptors are the first candidate to contribute to color constancy. From

our experience of coming from the outside into a dark room or vice versa,

we know that the visual system is able to adapt to darkness and brightness.

This ability also holds in situations where the color hue of the surrounding

illumination changes. Von Kries (1905) suggested that the visual system is

able to adapt to the surrounding illumination, and that this adaptation is

simply an appropriate scaling of the receptor responses that result from a

viewed stimulus. In detail, if the illuminant mainly consists of long–wave

light, mainly the receptor which is sensible to long–wavelength light becomes

scaled. If the illuminant mainly consists of short–wavelength light, mainly

the receptor which is sensible to short–wave light becomes scaled. Early stud-

ies tested this suggestion experimentally. Hurvich & Jameson (1958) used

simple center–surround stimuli, where some test light was presented against

a uniformly colored background. The task of the observer was to match a

second light, presented against a second, differently colored background, to

the test light. The illuminants were simulated through the colors of the back-

ground. It was found that the von Kries principle failed. Hence, the authors

proposed a two–stage adaptation model where an additional additive process

at the opponent color site modifies the scaled receptor signals. However, it

was later shown that the failure of the receptor scaling principle was due to

the binocular presentation of the stimuli, and that it was more the recep-

tor responses of the center relative to the surround that were scaled, rather

than the receptor responses of the center itself (Walraven, 1976; Werner &

Walraven, 1982).


It was shown later that the findings with the simple center–surround

paradigm could be generalized to more complex stimuli. Brainard & Wan-

dell (1992) used more natural stimuli, so–called Mondrian patterns. The

uniform surround representing the illuminant was replaced by a number of

rectangular, differently colored patches. These patches were CRT simulated

matte surfaces, uniformly illuminated by some simulated light. By testing

several models to describe the form of visual adjustment to the illuminant,

the authors could show that the fit of the simple von Kries receptor scaling

model was as good as the fit of other more general models. Bauml (1995) also

used Mondrian stimuli and tested the hypothesis that the site of adjustment

to illumination is at opponent color stage rather than at receptor stage. He

showed that an adjustment of opponent color signals provided a much worse

description of his data than an adjustment of receptor signals.

Receptor scaling has turned out to be a good model to describe experi-

mental data of color constancy studies. However, it is silent about how these

scalings depend on illuminant changes. Brainard & Wandell (1992) were able

to identify another principle. They conducted a successive color matching

experiment and showed that the scalings depend linearly on changes in illu-

mination. They called this principle illuminant linearity. If the adjustment

for two illuminant changes is known, the adjustment for a third illuminant

change can be predicted by a linear combination of the two. Bauml (1995)

and Chichilnisky & Wandell (1995) were able to confirm their results and

extended them to a wider range of viewing contexts.

There is some empirical evidence that at least the von Kries principle

is not only valid in simulated Mondrian worlds but also holds in real–world

situations. Brainard, Brunt, & Speigle (1997) used real papers rendered

under real illuminants rather than CRT simulated illuminants and surfaces.


They measured color appearance in a simultaneous color constancy situation,

where stimuli were presented side by side, and found good evidence for the

von Kries principle. These studies indicate that receptor scaling plays a

major role in adjusting to ambient illumination.

In addition to the validity of the receptor scaling principle, Brainard et al.

(1997) found a color constancy index of about 60%. This is rather high when

compared to similar simultaneous color constancy paradigms with simulated

scenes, where constancy is on the order of 25% for color appearance (Arend

& Reeves, 1986; Bauml, 1999a). Brainard (1998) examined successive color

constancy in real–world scenes with an achromatic adjustment paradigm. He

found a color constancy index of 82%. This is again much better constancy

than typically obtained in analogous CRT–simulated Mondrian scenes, where

constancy is about 50–60% (e. g. Brainard & Wandell, 1992; Bauml, 1994).

Kraft & Brainard (1999) found a similar degree of color constancy in a rich

real scene. The differences between real and simulated stimuli might be

due to additional clues that are present in real–world scenes, which help

the visual system to adjust better to the illuminant. It was also suggested

that the visual system treats real and simulated stimuli different (Brainard

et al., 1997). However, even in rich, three–dimensional real–world scenes

rendered on a computer monitor, color constancy is higher than in classical

flat Mondrian worlds (Delahunt & Brainard, 2004a).

The von Kries principle and illuminant linearity are substantiated rather

well. They are considered to be low–level sensory processes. However, other

higher–level mechanisms were identified that support the visual system in

situations where sensory processes are of limited use for holding colors con-

stant.


2.3.2 Perceptual processes

Von Kries adaptation proposes a single low–level mechanism: a simple scal-

ing of the receptor signals. However, there is strong evidence that processes

at higher perceptual levels have a large influence on how we perceive color.

As mentioned in chapter 1, there are two different types of color codes, one

referring to apparent color and one referring to object color. Arend & Reeves

(1986; see also Arend, Reeves, Schirillo, & Goldstein, 1991) showed that the

two types of color codes can be evoked just by giving the appropriate in-

struction to the observer. They carried out a simultaneous asymmetric color

matching task presenting two Mondrian patterns side by side. They gave

the observers one of two instructions. Either they were supposed to match

hue, saturation, and brightness, i. e. the apparent color, of the matching

surface to the test surface (appearance match), or they were supposed to

set the match so that test and matching surface looked as if they were cut

from the same piece of paper (surface match). The authors found relatively

low color constancy of about 20% when observers were asked to make ap-

pearance matches, and relatively high color constancy of about 78% when

asked to make surface matches. It is important to note that in simultaneous

color constancy situations adaptational processes are excluded to a large ex-

tent, reducing low–level von Kries adaptation. Thus, the low constancy for

color appearance is not surprising. However, the visual system is nonethe-

less able to compensate for illuminant changes concerning surface color to a

fairly large extent. This ability has hence to be attributed to higher–level

perceptual processes that are important for judging color in our everyday

life.

In most three–dimensional scenes we encounter more than one illuminant.


Shadows, mutual reflections or multiple direct illuminants generate a fairly

complex image, where low–level von Kries adaptation can only fail. The

facility to perceptually separate apparent color from surface color supports

the visual system in achieving color constancy in situations where sensory

processes are of limited use.

From the results of the studies mentioned above, it might be concluded

that the visual system must be able to somehow estimate the illumination to

extract approximately correct color codes. Helmholtz (1866) suggested that

the visual system disentangles the effects of illuminant and surfaces by esti-

mating the illuminant and discounting it. In his view, color is generated by

higher–level judgment rather than adaptation. Several cues to the illuminant

within scenes have been identified, e. g. specular highlights, mutual reflec-

tions and spatial chromatic mean of the image, and there is evidence that the

visual system combines them to achieve color constancy. Kraft and Brainard

(1999) measured successive color constancy in nearly natural scenes. While

successively reducing cues to the illuminant in the scenes, they observed a

decline in the degree of constancy. Their results suggest that the illuminant

is indeed estimated by the visual system.

In a rather different approach, it is assumed that there is no need for the

visual system to estimate the surrounding illumination. It was computation-

ally shown that, within receptor class, cone–excitation ratios from a pair of

illuminated surfaces are almost invariant under changes of daylight illuminant

(Foster & Nascimento, 1994). It was also shown that even in highly reduced

experimental setups where no utilizable cue to the illuminant in the scene is

given there is a considerable amount of color constancy. Amano, Foster, &

Nascimento (2005) presented two Mondrians side by side in a simultaneous

color constancy paradigm. Each of the patterns consisted of only two sur-


faces whereas one surface of one of the patterns served as the match surface.

Observers were asked to make surface matches. Though it was impossible

to estimate the illuminant in such a situation, the degree of color constancy

was almost as high as in richer scenes with patterns of 49 surfaces. The au-

thors proposed the invariance of cone–excitation ratios as the explanation of

the results. This invariance yields the concept of relational color constancy

(Craven & Foster, 1992). Craven & Foster (1992) developed an interesting

approach to examine the concept of relational color constancy. They argued

that it is vital for a human visual system to be able to discriminate whether

a change of a scene is due to a change of illumination or due to a change in

surfaces. Indeed, this is the case in situations where an illuminant changes

abruptly, e. g. by switching a tungsten bulb on or off in a room already illu-

minated by daylight (see section 1.1). The authors presented two identical,

yet differently illuminated, Mondrians in rapid succession. In some of the

trials, there was an additional change in surfaces between the two stimuli.

They asked observers to judge whether a change in illuminant or a change

in surfaces occurred. They found that observers were able to make these

judgments reliably and effortlessly.

The evidence of the physical invariance of cone–excitation ratios under

illuminant changes is striking and offers an alternative to explain findings

from several simultaneous color constancy studies. However, it is the task of

physiological research to examine which site of color processing accounts for

the ability to achieve constant surface colors.

Nowadays, there is high agreement that color constancy is not mediated

by a single mechanism but by a combination of low–level adaptational and

higher–level perceptual mechanisms (see Kaiser & Boynton, 1996). In addi-

tion, there is evidence that even cognitive mechanisms influence the apparent


color of objects.

2.3.3 Cognitive processes

In recent years, support has emerged for the hypothesis that cognitive pro-

cesses play a role in color perception. Hurlbert & Ling (2005) tested color

memory for a real known object, a banana. In symmetric and asymmetric

memory matching tasks, they found that the color match of the banana was

shifted towards a too saturated yellow, while matches of color chips did not

produce such a shift. While Hurlbert and Ling presented color chips for

observers to choose from to make a match, Hansen et al. (2006) used achro-

matic adjustment as a measure for color memory. They asked observers to

adjust the colors of simulated fruits and vegetables until they appeared grey.

Similar to Hurlbert & Ling (2005), their results showed a shift of adjustment

towards the opponent colors of the objects. For example, the adjustment for

the banana was a slight blue, while the adjustment for a cabbage patch was

a slight red. Achromatic adjustments of simple color chips, however, were

close to the neutral grey point. These studies show that color memory of

well–known objects has a considerable effect on color perception and helps

us recognize the colors of objects.

2.4 Measuring color constancy

Apparent color and object — or surface — color was investigated using var-

ious experimental approaches. Experimenters typically use CRT–simulated

surfaces and illuminants as experimental stimuli. As a paradigm, asymmet-


ric color matching3 is often employed. Observers are shown a set of grid–like

arranged, rectangle, matte surfaces, so–called Mondrian patterns, which are

illuminated by some light.

Apparent color can be measured both under successive and simultaneous

color constancy conditions. In successive situations, observers have to mem-

orize the color of a particular surface after visually adapting to the Mondrian

pattern. After that, the same Mondrian is shown again but illuminated by

a different light. After adapting to this new stimulus, observers have to ad-

just the apparent color of a particular surface in terms of hue, saturation,

and brightness to make a match to the memorized color (e. g. Brainard

& Wandell, 1992). A second popular paradigm is called achromatic adjust-

ment. Here, the task for the observer is to adjust hue and saturation of a

certain patch until it appears achromatic, i. e. until it appears neither bluish

nor yellowish nor reddish nor greenish. Again, this is done successively un-

der two different illuminants. In simultaneous color constancy situations,

the two differently illuminated Mondrian patterns are presented side by side.

The observer is asked to look back and fourth between the patterns to reduce

adaptation to any of the stimuli. The task for the observer is to match hue,

saturation, and brightness of a particular patch of the, say, right pattern to

the corresponding patch of the left pattern (Arend & Reeves, 1986).

Surface color is typically measured in simultaneous color constancy sit-

uations. Two patterns are presented side by side, each rendered under a

different illuminant. Observers are asked to match the color of a particular

surface in one pattern to the color of the related surface in the other pattern.

However, instead of adjusting the apparent color in terms of hue, saturation,

3The paradigm of asymmetric color matching is based on that of symmetric color

matching, which is described in chapter 2.1.


and brightness, observers are asked to adjust the surface color so that it

seems as if the two patches were cut from the same piece of paper (Arend &

Reeves, 1986). It should be noted that the apparent colors of the two patches

are usually different in this situation.

For both apparent and surface color, color constancy is usually measured

with an index ranging from 0 to 1. The index is 0 when no constancy is

observed, and 1 when perfect color constancy is found.

In the third situation described in the preceding section, the illuminant

changes rapidly over time. The visual system must be able to assign the

resulting change in apparent colors correctly to either a change in illuminant

or to a change in surfaces. An interesting way to investigate this ability is

the operational approach developed by Craven & Foster (1992). An observer

is briefly shown two illuminated Mondrians in succession, each for one sec-

ond. There is always an illuminant change between the two Mondrians and

sometimes an additional change in surfaces. The task for the observer is to

discriminate a pure change in illuminant from a change in surfaces. In the op-

erational paradigm, discriminating illuminant changes from surface changes

in a scene produces a class of constant color percepts (Foster, Nascimento,

Craven, Linnell, Cornelissen, & Brenner, 1997). In matching paradigms, the

corresponding class consists of all adjustments the observer is satisfied with.

The paradigms are related insofar as both try to identify and describe the

situations in which constant color percepts are yielded.

In the operational approach, color constancy can be measured in terms

of the discrimination index d’ (see chapter 4.4). The index is 0 when no

constancy is observed and approaches infinity if color constancy is perfect.


2.5 Summary

Results from psychophysical studies using the symmetric color matching

paradigm led to the suggestion that the human visual system encodes light

with three classes of photoreceptors, which are sensitive to short–wavelength

light, middle–wavelength light, and long–wavelength light, respectively. Psy-

chophysical hue cancellation experiments showed that the three resulting

signals are then recoded by opponent color mechanisms into light/dark,

red/green, and blue/yellow signals. The receptoral and opponent color mech-

anisms were also confirmed, at least in part, by finding physiological corre-

lates. It was further shown by fMRI studies that color signals are further

processed in the primary visual cortex.

The color constancy problem describes the mismatch between different

physical lights reaching the eye and perceptual equality of resulting color.

When an observer is looking at a surface illuminated by a light that slowly

changes over time, the apparent color of the surface remains roughly the

same, although receptor responses, in general, change with the illumina-

tion. When an observer is looking at a surface which is rendered under

an illuminant that changes spatially or temporally in a rapid manner, the

resulting light incidents at the eye are also different, yielding different pho-

toreceptor responses. In this situation, apparent color can only marginally be

maintained. However, the surface color code generated in the visual system

remains roughly the same.

Three stages can be identified where color constancy might be medi-

ated. First, sensory processes are assumed to scale photoreceptors in order

to achieve adjustment to a surrounding illumination. The so–called von

Kries adaptation could be demonstrated in simple center–surround situa-


tions, as well as with Mondrian patterns. In a rather different approach,

called relational color constancy, it was shown that — within receptor class

— cone–excitation ratios from a pair of illuminated surfaces are almost in-

variant under changes of illuminant, ruling out any need for the visual system

to adapt to the illuminant or to estimate it. Second, perceptual processes

are assumed to estimate the ambient illumination by using a range of differ-

ent cues typically present within a scene. In simultaneous color constancy

paradigms, it was shown that a high level of color constancy can be found

when observers were asked to regard all colors as surface colors instead of

apparent colors. Automatic adaptational processes are reduced in such a

paradigm, resulting in the assumption that the illuminant has to estimated

by the visual system. Third, cognitive aspects are assumed to have a consid-

erable effect on color perception. In fact, color memory was found to help us

recognize the colors of common objects.

Chapter 3

Color constancy under different

illuminants and surface

collections

3.1 Illuminants and surfaces in our environ-

ment

There are three classes of illuminants in our environment. First, daylight

illuminants are a mixture of sunlight and skylight, and vary from blue to

white to yellow, depending on daytime and weather conditions. Judd et al.

(1964) and DiCarlo & Wandell (2000) extensively measured spectral power

distributions of daylight at various daytimes and weather conditions. The

chromaticity coordinates of the daylights obtained by these measurements

form a point cloud in CIE u’v’ color space, and the fitted curve through

this cloud is called the CIE daylight locus (Wyszecki & Stiles, 1982). Fig-

36

CHAPTER 3. ILLUMINANTS AND SURFACE COLLECTIONS 37

ure 3.1 shows that coordinates of 10760 daylight measurements roughly fall

on a line. The basic shapes of spectral power distributions of daylights are

rather similar and can be approximated by a low–dimensional linear model.

It was shown that the first three basis functions derived from a principal

component analysis are sufficient to render these illuminants almost exactly

(Judd et al., 1964). Second, artificial illuminants include tungsten bulbs,

fluorescent lamps, as well as any other artificially produced illuminant. Even

though the spectral power distributions of artificial illuminants are different

from those of daylights, it is notable that common artificial illuminants have

chromaticity coordinates similar to that of daylights (Barnard, Martin, Funt,

& Coath, 2002). Third, indirect illumination arises through mutual reflec-

tions of light at surfaces. As opposed to daylights and common artificial

light sources, non–daylight illumination may have chromaticity coordinates

far off the daylight locus, as can be seen in Figure 4.1. In everyday environ-

ments, we are exposed to a great deal of illumination resulting from mutual

reflections at object surfaces. Such reflections alter the spectral composition

as well as the intensity of the original light. For example, in forest areas,

almost the entire illumination is indirect. A neutral daylight, say at noon,

is reflected various times by leaves or other greenish surfaces. The resulting

light which incidents at our eyes is then shifted towards green. Depending

on the direct illuminant and the reflecting surfaces, non–daylight illumina-

tion can have a broad range of colors. It has been shown that it takes up a

considerable proportion of the overall illumination within three–dimensional

scenes (Ruppertsberg & Bloj, 2007) and can notably affect color appearance

of three–dimensional objects (Langer, 2001). Non–daylight illuminants can

be simulated in different ways. Since there is no direct natural equivalent

to daylight illuminants, unique spectral power distributions corresponding


0.14 0.20 0.260.40

0.46

0.52

u’

v’

Figure 3.1: CIE u’v’ coordinates of 10760 daylights, measured by DiCarlo &

Wandell (2000). The solid line is the daylight locus.


to particular chromaticity coordinates do not exist. One way to construct

a non–daylight illuminant is to use the daylight basis functions (Delahunt

& Brainard, 2004a, 2004b). This is a convenient method used to construct

a wide range of non–daylight illuminants. However, some illuminants do

not lie within the three–dimensional model for daylight illuminants, result-

ing in spectral power distributions with negative power at some wavelengths.

This is an undesired feature, since such spectra only exist virtually. These

illuminants, lying mainly in the green area, can instead be constructed by

a three–dimensional model of the spectral power distributions emitted by

monitor phosphors. This method was used by Delahunt & Brainard (2004a,

2004b), who measured the basis functions of their laboratory monitor and

provided them as supplemental material of their studies.

Furthermore, illuminant changes in our environment might not only in-

volve changes in the relative spectral composition, i. e. the color hue, of the

light but also an additional change in light intensity. For example, when com-

ing out of a dark room to the outside into daylight, light intensity increases

by several times. Thus, color should be regarded as having an intensity

dimension in addition to the color hue dimensions.

Daylights and artificial lights are rather well–defined sets of illuminants,

since spectral power distributions of daylights vary smoothly along the day-

light axis and artificial illuminants have fixed and easily measurable spectral

power distributions. Surfaces in turn are defined by their spectral reflectance

functions, which do not represent a closed set as opposed to daylights, since

there is an almost infinite number of natural and artificial surface reflectances

(Nascimento, Ferreira, & Foster, 2002). Nascimento et al. (2002) made

640000 measurements of surface reflectance spectra in rural and urban scenes.

It is notable that chromaticity coordinates of the mean reflectance spectra in


rural scenes were shifted towards the green area compared to that of urban

scenes, which gathered largely along the daylight locus. Similar results for

natural scenes were obtained by Webster & Mollon (1997). Hendley & Hecht

(1949) made measurements for foliage and earth surfaces, which clustered

in a very small area in the green–yellow and yellow area, respectively. Bur-

ton & Moorhead (1987) measured reflectances of terrain scenes and found

their data points scatter mainly in the green area. The mean reflectance

had chromaticity coordinates of u’=0.191 and v’=0.473 which is a point that

lies in the green direction relative to that of CIE D65 standard illuminant.

Overall, spectral reflectances of urban scenes are rather equally distributed in

color space with mean chromaticities clustering along the daylight locus. Re-

flectances of rural scenes are distributed more in the green area with means

lying to the green side of the daylight locus. It is notable that, from the

mentioned measurements, by far the fewest reflectances fall to the red side

of the daylight locus.

Munsell tried to establish a classification system of a closed set of selected

surfaces. These surfaces are perceptually ordered and span a wide range of

spectral reflectances. The resulting Munsell Book of Color is considered

representative for all natural and artificial surfaces (Maloney, 1986) and is

widely used in color science. A representative subset of the Munsell surface

collection is used in this work. Since the shapes of reflectance functions

representing Munsell papers are not as similar as the set of spectral power

distributions of daylights, it is not possible to fit low–dimensional models well

enough to obtain acceptable results. However, it has been shown that five to

seven basis functions are sufficient to properly approximate the reflectance

functions of Munsell papers (Maloney, 1986).


3.2 Color constancy under different illumi-

nants

Most previous color constancy experiments used daylight illuminants as ex-

perimental stimuli (e. g. Brainard & Wandell, 1992; Bauml, 1999a; Craven

& Foster, 1992). However, there is a number of studies which compared

the degree of color constancy along the daylight axis and along other color

axes. Most of them examined the role of color direction in successive color

constancy situations, using asymmetric matching or achromatic adjustment.

Lucassen & Walraven (1996) found better constancy in the blue direction

than in the yellow direction using the neutral CIE D65 as a standard il-

luminant. Brainard (1998) used real illuminants and surfaces as stimuli.

He found only slight differences in color constancy along several color axes.

Ruttiger, Mayser, Serey, & Sharpe (2001) measured color constancy along

the daylight axis and the red–green cardinal directions in color space. They

found better color constancy along the red–green axis. Delahunt & Brainard

(2004a, 2004b) conducted a detailed study regarding the issue of color direc-

tion. They used a simulated three–dimensional room in order to investigate

successive color constancy in blue and yellow daylight color directions and

orthogonal red and green color directions. They found rather high constancy

along blue and green axes, mediocre constancy along the yellow axis, and

rather low constancy along the red axis.

Simultaneous color constancy was investigated using asymmetric match-

ing paradigms (e. g. Arend & Reeves, 1986; Bauml, 1999a). None of

these studies focused on constancy along different illuminant color direc-

tions. Bauml (1999a), however, compared observers’ appearance and surface

matches and found them to differ only in a quantitative but not in a qual-


itative way. This qualitative similarity of appearance and surface matching

might suggest similar constancy patterns along different color directions in

successive color constancy and in simultaneous color constancy situations.

Some studies investigated performance at discriminating illuminant changes

from surface changes using an operational paradigm similar to the one used

in this work. Observers were shown two differently illuminated Mondrian

patterns in succession. In some trials, an additional change in surfaces was

applied. The task was to discriminate trials where a pure illuminant change

occurred from trials where surfaces were changed. Foster, Amano, & Nasci-

mento (2003) and Amano, Foster, & Nascimento (2003) examined perfor-

mance in a blue and a green illuminant color direction and found similar

performance. There are some further studies which also used this or slight

variations of the discrimination paradigm (Craven & Foster, 1992; Foster,

Craven, & Sale, 1992; Nascimento, 1995; Nascimento & Foster, 1997; Nasci-

mento & Foster, 2000; Linnell & Foster, 2002; Foster, Amano, & Nascimento,

2001). However, there was no focus on performance along different illuminant

directions.

Besides color hue, another important attribute of illuminants is their in-

tensity. Most previous studies about color constancy either did not involve

luminance changes or did not control them systematically. However, Werner

& Walraven (1982) found an effect of luminance on the achromatic locus in an

achromatic adjustment paradigm involving chromatic adaptation. Their ex-

periment is somewhat related to successive color constancy studies, but very

simple center–surround stimuli rather than Mondrian patterns were used.

Brainard et al. (1997) examined simultaneous color constancy using a si-

multaneous matching paradigm and did not find an effect of luminance on

observers’ settings. They conducted their experiments in a room with real


illuminants and surfaces to simulate natural viewing conditions. There is

no experiment which investigates the role of luminance changes in situations

where illumination changes abruptly over time. In studies examining this

situation, luminance was either held constant (Craven & Foster, 1992; Foster

et al., 1992; Nascimento & Foster, 1997; Nascimento & Foster, 2000; Foster,

Amano, & Nascimento, 2001) or it was not controlled at all (Nascimento,

1995; Linnell & Foster, 2002; Foster et al., 2003; Amano et al., 2003). It

is notable that in almost every study investigating the role of illuminant

direction and luminance, considerable observer differences were found.

3.3 Color constancy under different surface

collections

A color constant visual system is able to maintain object colors despite

changes in surrounding illumination. To get along in different environments,

this feature must hold across a variety of scenes. Those scenes can, for in-

stance, be rural, forested, or urban. From our daily experience, our visual

system compensates well for illuminant changes without dependence on scene

surface composition. However, it has been mentioned above that there are

also irregularities in color constancy under illuminant changes with different

color directions which are hardly recognized in everyday life. Despite some

research on this issue we do not know exactly how different surface collections

influence the degree of color constancy.

There are a few studies that deal with the issue of the role of surface

collection for successive color constancy. Bauml (1994) examined achromatic

loci in successive color constancy situations and found them to vary with


surface collection. This effect was particularly large for surface collections

with rather different mean chromaticity coordinates. He also found slight ob-

server differences. Bauml (1999b) also found observers’ settings to vary with

surface collection with different mean chromaticities. He found a slight inter-

action of the effect of illuminant and the effect of surface collection. Bauml

(1995) tested successive color constancy under different surface collections

varying mainly in mean luminance rather than in mean chromaticity. He did

not find an effect of surface collection on the color matches, but again there

were individual differences. Brainard (1998) examined achromatic loci under

differently colored backgrounds. He found detectable but small differences

in adjustment.

Bauml (1999a) investigated apparent and surface color constancy in a si-

multaneous situation. He found almost no differences between color matches

under a neutral and a bright neutral collection, but some differences under a

neutral and a red collection and under a bright neutral and a red collection.

He compared results of his apparent and surface color matching paradigms

and found them to be rather similar in a qualitative way.

Apart from the role of illuminant color direction and surface collection,

it is important to investigate to which extent these two factors influence

each other. A slight interaction of illuminant direction and surface collection

was found by Bauml (1999a) in both apparent and surface color matching

situations. However, as the role of illuminant direction and surface collection

is not clear in situations with abrupt temporal illuminant changes, we do not

know if there is an interaction regarding the amount of visual adjustment.


3.4 Goals of the study

It was mentioned that there are studies showing at least slight effects of illu-

minant color direction and surface collection on the degree of color constancy.

The vast majority of studies investigated this issue in successive or simulta-

neous color constancy situations. The results are, however, rather contradic-

tory in regard to the pattern of constancy under different illuminants and

surface collections. This might be due to some observer differences found

along with a rather small number of tested observers. There is also some

research to date dealing with the color constancy situation in which an illu-

minant changes abruptly over time. However, most of them do not examine

constancy under different illuminant directions or surface collections.

This study is being done for two reasons. First, the influence of color

direction in illuminant changes, as well as the role of surface collection, is un-

clear in color constancy situations with abrupt temporal illuminant changes.

This gap is intended to be filled. If results from successive and simultaneous

color constancy studies generalize to situations with rapid temporal illumi-

nant changes, similar patterns would be obtained in this study. For instance,

the studies of Delahunt & Brainard (2004a, 2004b) show reliable effects of

illuminant direction on the degree of successive color constancy being high-

est in blue and green directions and lowest in the red direction. It was

shown above that in successive or simultaneous color constancy paradigms

the amount of visual adjustment in particular illuminant directions correlates

somehow with the frequency of occurrence of the respective illuminants in

our environment. If this feature is intrinsic to our visual system then similar

result patterns should show up in the present paradigm as well.

Second, it is not clear if the degree of color constancy depends on the


surface collection in situations with abrupt temporal illuminant directions.

Further, this issue was not investigated in detail with other paradigms. It

was shown that at least small effects were found in successive and simulta-

neous color constancy paradigms. If the amount of visual adjustment under

particular surface collections also correlate with the occurrence of surfaces

in natural environment then rather high constancy under a green, medium

under yellow and blue, and low constancy under a red collection would be

expected.

It should be noted that there is strong evidence for the validity of some

basic principles like the von Kries law or illuminant linearity. These principles

were tested under a large number of illuminant changes and surface collec-

tions and were confirmed rather well in a variety of viewing contexts. On the

other hand, some effects of illuminant direction and surface collection were

found. Since the models which were fitted in these studies seem to be rather

robust against such effects, the operational paradigm used throughout the

present study might provide detailed insights regarding to which extent the

visual system adjusts to illuminant changes along different color directions

and under different surface collections. If the expected results are obtained

in this study, however, the principle of illuminant linearity should be re-

viewed. Illuminant linearity states that an observers’ setting in a matching

paradigm depends linearly on the illuminant change. If the amount of visual

adjustment varies with the color direction of the illuminant change then this

principle may be challenged. Dependent on how strong such a result pat-

tern influences illuminant linearity, the findings should be incorporated in

the principle.

Chapter 4

General methods

4.1 Apparatus

All stimuli were generated by a ViSaGe Visual Stimulus Generator (Cam-

bridge Research Systems Ltd., U. K.) with a resolution of 8 bit per gun. A

DELL Precision 670 Minitower host computer with a VSG Toolbox (Cam-

bridge Research Systems Ltd., U. K.) was used for running the Matlab

programs and controlling the ViSaGe. Stimuli were presented on a 19”

RGB monitor (Mitsubishi Diamond Pro 2070SB) with a screen resolution of

1280x961. The monitor was calibrated before each experiment using a Col-

orCAL colorimeter (Cambridge Research Systems Ltd., U. K.). Observers

were sitting directly in front of the stimulus monitor viewed at a distance of

approximately 80 centimeters without a chin rest. Experiments were carried

out in a darkened room.

47

CHAPTER 4. GENERAL METHODS 48

4.2 Experimental illuminants and surfaces

Daylight as well as non–daylight illuminants were used in this work. Wyszecki

& Stiles (1982) provide an algorithm that maps an arbitrary point on the

daylight locus to the corresponding spectral power distribution using a three–

dimensional model. The daylight illuminants used in this work were drawn

out of this pool of spectral power distributions. Non–daylight illuminants

were constructed using the same daylight basis functions, or the monitor basis

functions of Delahunt & Brainard (2004a, 2004b) if illuminants lied outside

of the daylight model (see section 3.1). The daylight basis functions, as well

as the monitor basis functions, are plotted in Appendix A. All experimental

illuminants were sampled from 400 nm to 700 nm in 10 nm steps.

For experimental surfaces, the set of 226 spectral reflectance functions

used by Brainard & Wandell (1992) was chosen. These surfaces were simu-

lated flat Lambertian papers from the Munsell Book of Color — Matte Fin-

ish Collection and were approximated using a six–dimensional linear model

whose basis functions were the first six principal components of the data set

of Kelly, Gibson, & Nickerson (1943). Figure 4.1 shows the CIE u’v’ coordi-

nates of the entire surface set rendered under the D65 standard illuminant.

The six basis functions to model the reflectance functions of the set of sur-

faces used are plotted in Appendix A. The CIE u’v’ chromaticity coordinates

of the surfaces are also listed in Appendix A. All spectral reflectances were

sampled from 400 to 700 nm at 10 nm steps.


0.14 0.255 0.370.31

0.425

0.54

v’

u’

Figure 4.1: CIE u’v’ coordinates of the entire set of 226 experimental surfaces

under illuminant CIE D65 (open square).


4.3 General procedure

Throughout this work, the operational approach developed by Craven & Fos-

ter (1992), or slight modifications, were used. This paradigm is supposed to

investigate color constancy in situations with temporal abrupt illuminant

changes and was applied in a number of other studies (e. g. Foster et al,

1992; Nascimento & Foster, 1997; Amano et al., 2005). Each image was a

Mondrian pattern composed of 7x7 adjacent rectangular surfaces of equal

size against a dark background (Figure 4.3). The pattern (but not the back-

ground) was rendered homogeneously under one experimental illuminant. It

subtended 10.5 degrees of visual angle, vertically and horizontally. The stim-

ulus presentation in each trial consisted of two temporal intervals. In the

first interval, a Mondrian pattern was rendered under a standard illuminant.

In the second interval, the same Mondrian was presented, but the illuminant

underwent one of two types of changes. For the uniform illuminant change,

the illuminant was shifted along a certain color axis. For the non–uniform

illuminant change, the same uniform illuminant change was first applied. In

addition, a change in surfaces occurred. It was the goal of the non–uniform

illuminant shift to render a picture for the second interval that cannot be

created from the Mondrian in the first interval through a naturally occur-

ring uniform illuminant shift. To an observer, the uniform illuminant change

would appear as a pure change in illuminant between the two images, while

the non–uniform illuminant change would be best interpreted as a change in

surfaces. Figure 4.2 depicts two examples of illuminant and surface changes.

It can be seen that a uniform illuminant change was performed in both condi-

tions. Without a uniform illuminant change in the surface change condition,

an additional cue would have been given to the observer because, between


the images, there would have been an overall chromaticity shift in the illu-

minant change condition, but not in the surface change condition. With this

uniform illuminant change in both conditions, there was the same average

chromaticity shift. The intervals lasted one second each and were presented

immediately after each other.

After the presentation of the two images, observers were to decide whether

an occurring change between the two images was due to a change in illumi-

nant or a change in surfaces. They were to give their answers by pressing

one of two buttons on a response box. There was no time constraint, but all

observers gave their judgments almost immediately after presentation. After

the response, the next stimuli were calculated, leading to a total duration

of about 4s per trial. Figure 4.3 depicts the procedure of a typical stimulus

presentation.

For each experiment, observers had to participate in several sessions.

Within sessions, observers made several judgments in each experimental con-

dition. The duration of the sessions differed, but never lasted longer than 45

minutes with short intervening breaks. The first session of each experiment

was regarded as a practice session and was not included in the analysis.

In Experiment 1, a set of daylight illuminants, along with the set of 226

Munsell papers, served as experimental stimuli to measure color constancy

along the daylight axis, with additional changes in light intensity. In Experi-

ments 2 and 3, daylights as well as non–daylights and the same set of Munsell

papers were used to examine whether the degree of color constancy is dif-

ferent under differently colored illuminants. In Experiment 4, one daylight

and one non–daylight illuminant was used. The set of surfaces was split into

four differently colored subsets to investigate the role of surface collection for


change in illuminant

change insurfaces

change in illuminant

change insurfaces

standard illuminant

standard illuminant

Figure 4.2: Two examples of illuminant and surface changes. At first, the Mon-

drian is always rendered under the standard illuminant (center Mondrians). After

that, either a change in illuminant (left Mondrians) or a change in surfaces (right

Mondrians) occurs.


1 s

1 s

Response:illuminant change orsurface change?

Response:illuminant change orsurface change?

1 s

1 s

‘illuminant change‘ response button

‘surface change‘ response button

Figure 4.3: Stimulus presentation (two trials). Two equal Mondrians rendered

under different illuminants were presented immediately after each other. In addi-

tion to this illuminant change, an additional change in surfaces was introduced in

half of the trials. After each trial, observers were asked to decide whether a pure

change in illuminant or a change in surfaces occurred.


color constancy.

4.4 Data Analysis

In the paradigm used in this work, observers had to discriminate between

illuminant changes and surface changes. In this sense, it can be interpreted

as a signal detection paradigm. Uniform illuminant changes that occurred

in all trials were considered as noise, whereas additional non–uniform illumi-

nant changes were considered as the signal to detect. A Hit was therefore

a correctly classified surface change, and a False Alarm was an illuminant

change that was classified as a surface change. A classical discrimination

index d′ was computed from the difference of the z–transformed Hit Rates

(HR) and False–Alarm Rates (FAR):

d′ = z(HR)− z(FAR)

The discrimination index d′ was the measure for the degree of color constancy

in this paradigm.

Chapter 5

Experiments

5.1 Experiment 1: The role of luminance in

illuminant changes

Luminance plays an important role in our environment. Luminance of illumi-

nants, say daylights, can vary drastically depending on daytime and weather

conditions. When the sun gets covered by a cloud, for example, luminance

decreases considerably. Thus, when investigating illuminant changes, not

only chromaticity but also luminance of illuminants should be considered.

Most previous studies about color constancy either did not involve lumi-

nance changes or did not control them systematically. Werner & Walraven

(1982) examined successive color constancy and found an effect of luminance

on the achromatic locus, but they used center–surround stimuli rather than

Mondrian patterns. Brainard et al. (1997) controlled luminance in a simul-

taneous matching paradigm and found no effect on observers’ settings. They

conducted their experiments in a room with real illuminants and surfaces to

55

CHAPTER 5. EXPERIMENTS 56

simulate natural viewing conditions. In studies investigating surface color

constancy in situations with rapid temporal illuminant changes using the

operational approach of this work, luminance was held constant or was not

controlled at all (e. g. Craven & Foster, 1992; Nascimento, 1995; Nascimento

& Foster, 1997, 2000).

The following experiment is conducted for two reasons. First, the ex-

perimental setup which was adopted from Craven & Foster (1992) and used

throughout this work has to be validated. For this purpose, I will try to

replicate the findings of Craven and Foster’s Experiment 3. They found

that discrimination performance decreased with uniform illuminant change

magnitude and increased with non–uniform illuminant change magnitude.

Second, the role of luminance in illuminant changes is to be investigated.

The question is whether a change in luminance, in addition to a change in

illuminant chromaticity, affects the degree of simultaneous color constancy in

situations with rapid temporal illuminant changes. Since luminance generally

changes in this type of everyday situation, the degree of color constancy is to

remain roughly the same. The experiment is run under three conditions. The

chromaticity change condition is designed for the replication. The luminance

change condition serves as a control condition to assess observers’ discrim-

ination performance for scenes where illuminant changes consist solely of

luminance changes. The chromaticity+luminance change condition involves

illuminant changes where both chromaticity and luminance change. This

condition is to be compared to the chromaticity change condition in order to

investigate the influence of the additional luminance change on discrimina-

tion performance.


5.1.1 Methods

Observers

Three observers participated in this experiment, CA (the author), SW, and

EH. All had normal color vision as assessed by Ishihara color plates (Ishihara,

1917). All observers, except the author (CA), were naıve about the purpose

of the experiment.

Experimental stimuli

Two daylights were used as initial illuminants, D1 (x=0.250, y=0.255) and

D2 (x=0.370, y=0.376). The surfaces that the Mondrian patterns were com-

posed of were drawn randomly without replacement from the pool of 226

spectral reflectances. There were three conditions: chromaticity change, lu-

minance change, and chromaticity+luminance change. In the chromaticity

change condition, both images were on an average luminance of 4 cd/m2,

but individual surfaces varied around this value (0.65 to 8.81 cd/m2). In

luminance change and chromaticity+luminance change conditions, average

luminance of the first image was 4 cd/m2 (0.65 to 8.81 cd/m2), and average

luminance of the second picture was 16 cd/m2 (2.62 to 35.24 cd/m2). In the

luminance change condition, illuminant chromaticity was held constant.

Procedure

The first image was a Mondrian illuminated randomly either by illuminantD1

or D2. For the uniform illuminant change, the CIE x–coordinate of the initial


illuminant was shifted by 0.03, 0.06, or 0.09 CIE x–units1, respectively, the

shift being positive for initial illuminant D1 and negative for initial illuminant

D2. For the non–uniform illuminant change, the same uniform illuminant

change was applied. In addition, the illuminant of a random half of the

patches was shifted positively by either 0.01, 0.02, or 0.03 CIE x–units and

negatively for the remaining half. The magnitudes of all shifts were randomly

drawn for each trial. There were 216 trials in each session, divided into three

blocks with short intervening breaks. Observers made about 60 judgments

in each condition, i. e. for each combination of initial illuminant, uniform

illuminant shift and non-uniform illuminant shift.

5.1.2 Results

Figure 5.1 shows the results for each participant in the chromaticity change

condition. Rows represent data for single observers while columns represent

data for trials where initial illuminant was D1 or D2, respectively. Within

each panel, data points depict discrimination performance d’ as a function

of uniform and non–uniform illuminant change. Magnitude of uniform il-

luminant change is coded by blue diamonds, pink squares, and yellow tri-

angles, representing changes of ∆x=0.03, ∆x=0.06, and ∆x=0.09, respec-

tively. Magnitude of non–uniform illuminant changes ∆x=0.01, ∆x=0.02,

and ∆x=0.03 is shown on the x–axis. Overall performance is above chance

for all observers. It decreases as a function of magnitude of uniform illumi-

nant change and increases as a function of magnitude of non–uniform illu-

minant shift. This becomes evident once we regard uniform illuminant shift

1Since the daylight locus is approximately a line in the CIE xy chromaticity diagram,

illuminant shifts are labeled for convenience by their x–coordinates. The y–coordinates

may be calculated using the respective algorithms in Wyszecki & Stiles (1982).


3

1

2

0

-1

3

1

2

0

-1

3

1

2

0

-10.01 0.030.020.01 0.030.02

initial illuminant: D initial illuminant: D

disc

rimin

atio

nin

dex

d‘di

scrim

inat

ion

inde

xd‘

disc

rimin

atio

nin

dex

d‘

non-uniform change [∆x] non-uniform change [∆x]

CA

SW

EH

1 2

Figure 5.1: Results for the chromaticity change condition. Columns represent

data for initial illuminants D1 and D2. Discrimination performance d’ is plotted as

a function of uniform and non–uniform illuminant change. Magnitude of uniform

illuminant change is coded by blue diamonds, pink squares, and yellow triangles

representing changes of ∆x=0.03, ∆x=0.06, and ∆x=0.09, respectively. Magni-

tude of non–uniform illuminant change is shown on the x–axis. Error bars show

± 1 SEM.


as noise and non–uniform illuminant change as signal in this psychophysical

discrimination paradigm. Performance then is a function of the signal–to–

noise ratio. The result pattern is very similar to that obtained in Experiment

3 of Craven & Foster (1992), thus their results could be replicated. The au-

thors did not provide a statistical analysis of their data. The analysis of

this replication, however, is included in the comparison analysis with the

chromaticity+luminance condition below.

Figure 5.2 shows discrimination performance of each participant in the

luminance change condition, which served as a control condition in order to

assess performance when solely luminance but not chromaticity changed. A

within–subject two–way ANOVA was conducted. There is an effect of ini-

tial illuminant for observer CA (F=13.61, MSE=0.19, p=0.01), a marginal

effect for SW (F=6.12, MSE=0.81, p=0.07), but no effect for EH (F=0.39,

MSE=0.75, p=0.57). Discrimination performance increases significantly as

a function of magnitude of non–uniform illuminant change for all three ob-

servers (CA: F=15.46, MSE=0.31, p=0.001; SW: F=20.69, MSE<0.01, p<0.01;

EH: F=38.25, MSE=0.08, p<0.01). There is also a significant interaction for

CA (F=5.15, MSE=0.39, p=0.03) and SW (F=15.92, MSE<0.01, p<0.01),

but not for EH (F=0.13, MSE=0.03, p=0.88).

Figure 5.3 shows the discrimination performance for each participant in

the chromaticity+luminance change condition. Data coding is the same as

in Figure 5.1. Discrimination, again, increases as a function of magnitude of

non–uniform illuminant change. However, the effect of uniform illuminant

change seems not as evident as in the chromaticity change condition. In Fig-

ure 5.4, data from Figures 5.1 and 5.3 was replotted in a scatterplot for better

comparison of chromaticity change condition and chromaticity+luminance

change condition in order to examine a possible effect of luminance on perfor-


3

1

2

0

-1

3

1

2

0

-1

3

1

2

0

-10.01 0.030.020.01 0.030.02


disc

rimin

atio

nin

dex

d‘di

scrim

inat

ion

inde

xd‘

disc

rimin

atio

nin

dex

d‘


CA

SW

EH

CA

1 2

Figure 5.2: Results for the luminance change condition. Columns represent data

for initial illuminants D1 and D2. Discrimination performance d’ is plotted as a

function of non–uniform illuminant change. Error bars show ± 1 SEM.


3

1

2

0

-1

3

1

2

0

-1

3

1

2

0

-10.01 0.030.020.01 0.030.02


disc

rimin

atio

nin

dex

d‘di

scrim

inat

ion

inde

xd‘

disc

rimin

atio

nin

dex

d‘


CA

SW

EH

CA

1 2

Figure 5.3: Results for the chromaticity+luminance change condition. Columns

represent data for initial illuminants D1 and D2. Discrimination performance d’ is

plotted as a function of uniform and non–uniform illuminant change. Magnitude

of uniform illuminant change is coded by blue diamonds, pink squares, and yellow

triangles representing changes of ∆x=0.03, ∆x=0.06, and ∆x=0.09, respectively.

Magnitude of non–uniform illuminant change is shown on the x–axis. Error bars

show ± 1 SEM.


Vergleich d´ Replikation vs Hauptexperiment

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0d´ chromaticity change

d´ c

hrom

atic

ity+l

umin

ance

cha

nge

E=0.03/R=0.01E=0.06/R=0.01E=0.09/R=0.01E=0.03/R=0.02E=0.06/R=0.02E=0.09/R=0.02E=0.03/R=0.03E=0.06/R=0.03E=0.09/R=0.03

Figure 5.4: Comparison of performances in chromaticity change and chromatic-

ity+luminance change conditions. Each data point from Figure 5.1 is plotted

against its corresponding data point from Figure 5.3. Magnitude of uniform il-

luminant change is coded by colors, blue, pink, and yellow, representing changes

of ∆x=0.03, ∆x=0.06, and ∆x=0.09, respectively. Magnitude of non–uniform il-

luminant shift is coded by size, small, medium, and large, representing shifts of

∆x=0.01, ∆x=0.02, and ∆x=0.03, respectively.


mance. Each data point from Figure 5.1 is plotted against its corresponding

data point from Figure 5.3. Magnitude of uniform illuminant shift is coded by

colors, blue, pink, and yellow, representing shifts of ∆ x=0.03, ∆x=0.06, and

∆x=0.09, respectively. Magnitude of non–uniform illuminant shift is coded

by size, small, medium, and large, representing shifts of ∆x=0.01, ∆x=0.02,

and ∆x=0.03, respectively. The correlation between data of the two con-

ditions is medium (r=0.55). If corresponding performances for all possible

combinations of uniform and non–uniform illuminant changes were equal in

both conditions, all data points would fall on the diagonal. There are clear

deviations from that. However, data points scatter rather evenly around the

diagonal, indicating similar mean performances in both conditions across ob-

servers and illuminant changes. There are three major outliers, one medium

and two large blue circles on the right, indicating some better performance

in the chromaticity change condition when signal–to–noise ratio is high and

the task is rather easy.

A within–subject 4–way ANOVA with the factors condition, initial il-

luminant, uniform illuminant change magnitude, and non–uniform illumi-

nant change magnitude was conducted to investigate discrimination perfor-

mance d’ of each observer. For all observers performance across conditions

do not differ (CA: F=0.08, MSE=1.60, p=0.80; SW: F=2.18, MSE=1.31,

p=0.24; EH: F=3.21, MSE=0.25, p=0.15). There is also no effect of ini-

tial illuminant (CA: F=0.01, MSE=0.58, p=0.93; SW: F=3.68, MSE=0.34,

p=0.15; EH: F=0.53, MSE=0.46, p=0.51). An effect of uniform illumi-

nant change magnitude was found for observer EH (F=8.25, MSE=0.54,

p=0.01) and marginally for observer SW (F=4.27, MSE=0.69, p=0.01), but

not for observer CA (F=2.05, MSE=0.99, p=0.19). However, there is a

large effect of non–uniform illuminant change magnitude for all observers


(CA: F=37.55, MSE=0.38, p<0.01; SW: F=17.32, MSE=0.22, p=0.003; EH:

F=30.48, MSE=0.32, p<0.01). A significant interaction of condition and

uniform illuminant change magnitude was found for observer EH (F=10.24,

MSE=0.35, p=0.01), a marginal interaction for observer CA (F=3.60, MSE=0.45,

p=0.08), and no interaction for observer SW (F=0.15, MSE=0.06, p=0.86).

A significant interaction of condition and non–uniform illuminant change

magnitude was found for observer EH (F=7.28, MSE=0.07, p=0.03), but not

for observers CA (F=0.34, MSE=0.07, p=0.72) and SW (F=0.26, MSE=0.20,

p=0.78). All in all, discrimination performance was similar across chromatic-

ity change and chromaticity+luminance change conditions.

5.1.3 Discussion

Two major results stand out. First, Experiment 3 of Craven & Foster (1992)

could be replicated, thus validating the experimental setup used in this work.

Discrimination performance increases with increasing signal–to–noise ratio,

determined by uniform and non–uniform illuminant change magnitudes. Sim-

ilar results were also found in another replication by Nascimento (1995). The

results show that observers are able to reliably discriminate between an il-

luminant change and a change in surface material in a scene. This is an

important feature in everyday life, since, for example, we have to be able to

tell whether or not objects in a scene retain their color when they are rapidly

illuminated in succession by two different lights. Second, color constancy is

not impaired if a luminance change in addition to a chromaticity change is

introduced.

Werner & Walraven (1982) examined successive color constancy and found

an effect of luminance. However, they used simple center–surround stimuli


instead of Mondrian patterns. Brainard et al. (1997) investigated color con-

stancy in a simultaneous situation using real–world stimuli. He did not find

an effect of luminance on observers’ settings. The findings, that luminance

changes do not have a major impact on the degree of color constancy in a

simultaneous matching paradigm as well as in the present paradigm, may

contribute to the view that luminance and chromaticity are processed differ-

ently in the visual system and that these processes are largely independent

from one another (see Kaiser & Boynton, 1996). The present results sug-

gest that this seems further to account for processes responsible for color

constancy. It was shown that discrimination performance deteriorates with

increasing uniform illuminant change magnitude in this paradigm. With an

additional change in luminance, this magnitude was further increased. How-

ever, the effect of such an additional luminance change is at best small. It

is an important feature of the visual system to maintain color constancy in

the present situation where an additional change in luminance is involved

because most illuminant changes in our environment are a combined change

in chromaticity and luminance. However, it is not clear if the present results

generalize to successive and simultaneous color constancy situations. Further

research has to be done on this issue to draw firm conclusions.

5.2 Experiment 2: The role of color direction

in illuminant changes

Illuminant colors in our environment can vary widely in color space. Daylight

varies from blue to white to yellow, but many scenes are not at all or at

least not solely illuminated directly by it. Depending on the reflectance


properties of a scene, the color of the direct daylight illuminant can be shifted

in different directions (Figure 4.1). Thus, we are surrounded by variously

colored illuminants, which all have to be considered for color constancy.

There is a number of studies which compared the degree of color constancy

along the daylight axis and along other color axes. Most studies examined

successive color constancy using either asymmetric color matching or achro-

matic adjustment. Lucassen & Walraven (1996) found better constancy in

the blue direction than in the yellow direction. Brainard (1998) found only

slight differences in color constancy along several color axes. Ruttiger et al.

(2001) measured color constancy along the daylight axis and the red–green

cardinal directions in color space. They found better color constancy along

the red–green axis. Delahunt & Brainard (2004a, 2004b) conducted the cur-

rently most promising study regarding the issue of color direction. They

used achromatic adjustment and a CRT–rendered three–dimensional room

in order to investigate color constancy in blue and yellow daylight color di-

rections and orthogonal red and green color directions. They found rather

good constancy along blue and green axes, mediocre constancy along the

yellow axis, and rather bad constancy along the red axis. Until now, no

study has focussed on the role of illuminant direction in a simultaneous color

constancy situation. However, Bauml (1999a) compared observers’ apparent

and surface color settings in a simultaneous situation and found them to be

similar in a qualitative way. Foster et al. (2003) and Amano et al. (2003)

investigated color constancy under rapid temporal illuminant changes using

a discrimination paradigm similar to the one used in this work. They found

similar performance in the green and blue direction.

The following experiment was carried out for two reasons. First, previous

studies produced mixed results. This might be due to individual observer


differences in the degree of color constancy along different color axes. Such

an observer effect might also be apparent in the operational paradigm used

in this work. This experiment tries to overcome this by using five observers.

Second, Delahunt and Brainard (2004a, 2004b) found an effect of color direc-

tion on the degree of successive color constancy while using a larger number

of seven observers. It is not clear if this pattern shows up in this discrimina-

tion paradigm as well. No experiment using the present paradigm considered

this issue directly. However, if the effect of color direction is an intrinsic fea-

ture of the visual system, a similar pattern should show up in the present

paradigm. The results of this experiment might then help to see how closely

related they are to results of successive color constancy paradigms, regarding

the relative amount of visual adjustment under different illuminant changes.

This experiment consists of two parts, Experiment A and Experiment

B. Experiment A uses the four illuminants formerly used by Delahunt &

Brainard (2004a, 2004b) in order to make the results comparable to their

study. Experiment B uses four additional illuminants to examine the pattern

of color constancy performance along different color axes in more detail.

5.2.1 Methods

Observers

Five observers participated in this experiment, CA (the author), EH, OK,

SW, and TD. All had normal color vision as assessed by Ishihara color plates

(Ishihara, 1917). All observers, except the author (CA), were naıve about

the purpose of the experiment.



CIE D65 was used as the initial illuminant. For Experiment A, the four

illuminants used by Delahunt & Brainard (2004a, 2004b) served as test il-

luminants. Figure 5.5 (upper panel) and Table 5.1 show their chromaticity

coordinates in CIE u’v’ color space. This space is approximately perceptu-

ally uniform, so equal Euclidean distances in the diagram roughly represent

equal perceptual distances. The distance from the initial illuminant to each

test illuminant is 60 CIELab ∆E∗ units, so the test illuminants are named

Blue60, Yellow60, Red60, and Green60. The spectral power distributions

of Blue60, Yellow60, and Red60 were constructed using the daylight basis

functions, Green60 was constructed using monitor basis functions.

For Experiment B, four additional illuminants were used. Their CIE u’v’

chromaticity coordinates were constructed to lie, respectively, exactly be-

tween illuminants used in Experiment A, with an equal distance of 60 CIELab

∆E∗ units from the D65 illuminant. They were labelled RY60, YG60, GB60,

and BR60. Figure 5.5 (lower panel) and Table 5.1 show their chromaticity co-

ordinates in CIE u’v’ color space. The spectral power distribution of RY60

and BR60 were constructed using the daylight basis functions, YG60 and

GB60 were constructed using monitor basis functions. The surfaces which

the Mondrian patterns were composed of were drawn randomly without re-

placement from the pool of 226 spectral reflectances. The average luminance

of the images was held constant at 4 cd/m2, but individual surfaces varied

from 0.65 to 8.81 cd/m2.


0.12 0.20 0.280.38

0.46

0.54

u’

v’

0.12 0.20 0.280.38

0.46

0.54

u’

v’

Figure 5.5: CIE u’v’ chromaticity coordinates of test illuminants and standard

illuminant CIE D65 (black square). Upper panel: Illuminants for Experiment A

(Blue60, Yellow60, Red60, Green60). Lower panel: Illuminants for Experiment

B (RY60, YG60, GB60, BR60); for comparison illuminants of Experiment A are

depicted in grey.


Table 5.1: Experimental illuminants used throughout this work. Distance of each

test illuminant from standard illuminant CIE D65 in CIELab ∆E∗ units and CIE

u’v’ chromaticity coordinates are tabled.

Illuminant Distance CIE u’ CIE v’D65 — 0.199 0.467Blue60 60 ∆E∗ 0.185 0.419Yellow60 60 ∆E∗ 0.226 0.508Red60 60 ∆E∗ 0.242 0.450Green60 60 ∆E∗ 0.153 0.489RY60 60 ∆E∗ 0.242 0.484YG60 60 ∆E∗ 0.183 0.512GB60 60 ∆E∗ 0.155 0.450BR60 60 ∆E∗ 0.219 0.427Red30 30 ∆E∗ 0.221 0.460RY30 30 ∆E∗ 0.221 0.477Yellow30 30 ∆E∗ 0.212 0.489YG30 30 ∆E∗ 0.190 0.492Green30 30 ∆E∗ 0.174 0.479GB30 30 ∆E∗ 0.175 0.459Blue30 30 ∆E∗ 0.192 0.445BR30 30 ∆E∗ 0.210 0.446Red85 85 ∆E∗ 0.260 0.443RY85 85 ∆E∗ 0.263 0.489Yellow85 85 ∆E∗ 0.237 0.525YG85 85 ∆E∗ 0.179 0.535Green85 85 ∆E∗ 0.134 0.498GB85 85 ∆E∗ 0.133 0.439Blue85 85 ∆E∗ 0.179 0.399BR85 85 ∆E∗ 0.227 0.405


Procedure

The first Mondrian pattern was always illuminated by CIE D65. The illumi-

nant of the second pattern was randomly drawn from the respective pool of

four test illuminants. Between images either an illuminant change or a surface

change occurred randomly. In illuminant change trials, the second Mondrian

was simply illuminated by one of the test illuminants. In the surface change

condition, the same illuminant change occurred, but additionally chromatic-

ity coordinates of a random quarter of the surfaces were then shifted in the

illuminant change direction, a second quarter in the opposite direction, and a

third and fourth quarter in the two orthogonal directions, respectively. The

magnitude of these shifts was 0.03 units in CIE u’v’ space. There were 200

trials per session, divided into three blocks with short intervening breaks.

Experiments A and B were carried out successively. In each experiment,

each observer made 300 judgments per illuminant direction.

5.2.2 Results

Figure 5.6 shows the results of Experiment A for each of the five observers,

as well as mean results over observers. Discrimination index d’ is plotted

as a function of illuminant direction. A one–way ANOVA was conducted

for the five observers to examine discrimination performance across differ-

ent illuminant changes. There is an effect of illuminant direction on the

degree of visual adjustment for observers CA (F=6.13, MSE=0.17, p<0.01),

OK (F=4.48, MSE=0.22, p=0.02), and SW (F=9.12, MSE=0.24, p<0.01),

but not for observers EF (F=1.14, MSE=0.34, p=0.37) and TD (F=1.47,

MSE=0.42, p=0.26). Plots show different patterns of performance over sub-

jects. Color constancy in the yellow direction, for instance, exceeds constancy


3

1

2

0

3

1

2

0

3

1

2

0

disc

rimin

atio

nin

dex

d‘di

scrim

inat

ion

inde

xd‘

disc

rimin

atio

nin

dex

d‘

CA

meanTD

SWOK

EF

B GRY B GRYilluminant direction illuminant direction

Figure 5.6: Results for the five observers and mean results over observers. Dis-

crimination index d’ is plotted as a function of illuminant direction (B=Blue60,

Y=Yellow60, R=Red60, G=Green60). Error bars show ± 1 SEM.


in the blue direction for observers CA, EF, and TD, but the opposite is true

for observers OK and SW. There is also a larger variation in performance

in the red direction across observers, while performance in blue and green

directions are rather stable across observers. A re–analysis of the data with

observer as a factor was carried out. The factors are observer (CA, EF, OK,

SW, TD) and illuminant direction (Blue60, Yellow60, Red60, Green60). The

replication is repeated measurements for each observer. There is a marginal

effect of observer (F=2.52, MSE=0.82, p=0.07), indicating some differences

in performance across observers. There is again an effect of illuminant di-

rection (F=6.27, MSE=0.32, p<0.01). The significant interaction (F=3.00,

MSE=0.80, p=0.03) confirms differences in the performance patterns across

observers, which are visible in Figure 5.6. The lower right panel of Figure

5.6 shows the effect of illuminant direction over observers. There is compar-

atively high performance in blue and green directions, mediocre performance

in the yellow direction, and rather low performance in the red direction.

To examine whether False Alarm rates of individual observers as well as

of the mean vary across conditions, these are listed in Table 5.2. It can be

seen, that False Alarm rates vary widely with illuminant direction. However,

there is no evidence that they correlate with discrimination performance.

For instance, observer CA has approximately equal discrimination indices of

about 1.5 under the yellow and green illuminant, but rather different False

Alarm rates of 0.07 and 0.25. In turn, he has similar False Alarm rates

of 0.30 and 0.31 under the blue and red illuminant, but rather different

discrimination indices of about 1.3 and 0.6. Analysis of the data of the other

observers as well as of the mean produces similar results.

Results for each observer participating in Experiment B, as well as mean

performance over observers, are shown in Figures 5.7–5.12. Upper panels


disc

rimin

atio

nin

dex

d‘

YR GYG GB BRBRY0

1

2

3

u‘

d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

CA d‘ = 3

illuminant direction

v‘

Figure 5.7: Results for observer CA. Upper panel: Polar plot within CIE u’v’

coordinate system. The filled circle represents u’v’ coordinates of CIE D65, di-

rection from the center represents color direction in CIE u’v’ space, and distance

from the center represents discrimination index d’. Lower panel: Bar plot for the

same data. Illuminant shift magnitude is 60 ∆E∗ units. Error bars show ± 1

SEM. Data from Experiment A is reprinted for comparison.


disc

rimin

atio

nin

dex

d‘

YR GYG GB BRBRY0

1

2

3

d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

EF d‘ = 3


u‘

v‘

Figure 5.8: Results for observer EF. Upper panel: Polar plot within CIE u’v’







disc

rimin

atio

nin

dex

d‘

YR GYG GB BRBRY0

1

2

3

d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

OK d‘ = 3


u‘

v‘

Figure 5.9: Results for observer OK. Upper panel: Polar plot within CIE u’v’







disc

rimin

atio

nin

dex

d‘

YR GYG GB BRBRY0

1

2

3

d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

SW d‘ = 3


u‘

v‘

Figure 5.10: Results for observer SW. Upper panel: Polar plot within CIE u’v’







disc

rimin

atio

nin

dex

d‘

YR GYG GB BRBRY0

1

2

3

d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

TD d‘ = 3


u‘

v‘

Figure 5.11: Results for observer TD. Upper panel: Polar plot within CIE u’v’







disc

rimin

atio

nin

dex

d‘

YR GYG GB BRBRY0

1

2

3

d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

d‘ = 3


u‘

v‘

mean

Figure 5.12: Mean results over observers. Upper panel: Polar plot within CIE

u’v’ coordinate system. The filled circle represents u’v’ coordinates of CIE D65,

direction from the center represents color direction in CIE u’v’ space, and distance





Table 5.2: False Alarm rates across illuminant directions of Experiment 2A for

individual observers as well as for the mean.

Observer Blue Yellow Red GreenCA 0.30 0.07 0.31 0.25EF 0.70 0.09 0.60 0.05OK 0.29 0.17 0.29 0.15SW 0.42 0.02 0.10 0.03TD 0.59 0.09 0.59 0.06mean 0.46 0.09 0.38 0.11

show data in a polar plot within Cartesian CIE u’v’ coordinates. The cen-

ter of the plot represents the chromaticity coordinates of D65 in CIE u’v’

space. The distance of each data point from the center depicts discrimi-

nation index d’, while the direction of each data point from the center is

equal to the illuminant change direction from the standard to the respec-

tive test illuminant in CIE u’v’ color space. Lower panels show bar plots

similar to Figure 5.6 of Experiment A. Plots include data from Experiment

A. The plots show some observer differences in the overall pattern of color

constancy in different illuminant directions. A one–way ANOVA for the

five observers was conducted over data from both Experiments A and B to

capture the effect of illuminant direction (Red60, Red–Yellow60, Yellow60,

Yellow–Green60, Green60, Green–Blue60, Blue60, Blue–Red60) on discrim-

ination performance. There is a significant effect of illuminant direction for

each observer (CA: F=7.22, MSE=0.15, p<0.01; EF: F=2.34, MSE=0.25,

p=0.05; OK: F=2.72, MSE=0.18, p=0.02; SW: F=5.08, MSE=0.22, p<0.01;

TD: F=2.64, MSE=0.25, p=0.03). To capture differences across observers,

a re–analysis of the data with observer as an additional factor was carried

out. Similar to Experiment A, there is a marginal effect of observer (F=2.18,


Table 5.3: False Alarm rates across illuminant directions of Experiment 2B for

individual observers as well as for the mean.

Observer RY YG GB BRCA 0.15 0.10 0.16 0.52EF 0.55 0.03 0.31 0.86OK 0.15 0.31 0.15 0.22SW 0.24 0.03 0.09 0.36TD 0.38 0.07 0.13 0.75mean 0.29 0.11 0.17 0.54

MSE=0.33, p=0.11), as well as a large effect of illuminant direction (F=7.86,

MSE=0.20, p<0.01), and a high interaction (F=2.74, MSE=0.21, p<0.01).

Figure 5.12 shows mean performances over observers. The graph (upper

panel) is approximately a circle which is widened towards the blue–green

direction and flattened in the red direction. The bar plot (lower panel) con-

firms the irregularities in terms of a smooth slope towards blue and green

and a decline in the red direction.

As for Experiment A, False Alarm rates of individual observers as well as

of the mean are examined and listed in Table 5.3. False Alarm rates again

vary widely with illuminant direction. However, there is again no evidence

that they correlate with discrimination performance.

5.2.3 Discussion

The purpose of this study was to find out if the degree of visual adjustment

depends on the color direction of a rapid temporal illuminant change, and if

results from studies using successive color constancy paradigms generalize to

this type of color constancy situation. In general, observers were again able


to reliably discriminate illuminant changes from surface changes. However,

different discrimination performances were found depending on illuminant

color direction. Foster et al. (2003) and Amano et al. (2003) found similar

constancy in the blue and green direction using a discrimination paradigm

similar to the one used in this work. Similar results were obtained here. It was

shown that False Alarm rates vary widely across illuminant directions but do

not correlate with discrimination performance. Therefore, False Alarm rates

do not help explaining the different discrimination indices across conditions.

It is an interesting question whether the results found in situations with

rapid temporal illuminant changes generalize to successive color constancy

situations. In a successive paradigm, Lucassen & Walraven (1996) found

better constancy along the blue than along the yellow axis. This finding is

consistent with the present results. Brainard (1998) found approximately

equal constancy in several color directions. However, he employed only two

observers, which led to a reduced experimental power. Ruttiger et al. (2001)

found better constancy along the red–green axis than along the daylight

axis. Their results are difficult to compare to the present findings since

performance is not split into semi–axes like neutral–green and neutral–red.

However, they in a way contradict the present results. When performance in

the blue and yellow direction and in the red and green direction is combined,

then constancy along the daylight axis exceeds that along the red–green

axis in the present experiment. Delahunt & Brainard (2004a, 2004b) found

high color constancy in the blue and green direction, mediocre constancy

in the yellow direction, and rather low constancy in the red direction using

seven subjects. They replicated their results several times and found them

reliable. Their results are consistent with the present results. Moreover, the

marginal effect of individual differences could be replicated. It seems that


the performance irregularities found here compare reasonably to patterns

obtained in successive color constancy situations.

The predominance of performance in blue and green illuminant direc-

tions is not easy to explain. In our natural environment, a rapid illuminant

change to the blue side occurs frequently when the sun is covered by a cloud.

A change to the yellow side occurs only during short periods at dusk and

dawn (Delahunt, 2001). Thus, taking D65 as the standard illuminant, the

probability of an illuminant change in the blue direction is higher than a

change in the yellow direction. This might explain the higher performance

in the blue direction relative to the yellow direction. The predominance

of the green direction might be explained by an evolutionary approach. It

was shown in section 3.1 that real–world scenes are mostly illuminated by

non–daylight illumination which arises from mutual reflections at surfaces.

For this reason, in forest areas, overall illumination is shifted towards green

(Endler, 1993). Given that our visual system developed in forest areas, it

might be argued that performance is rather high in the green direction.

In Experiment B, four additional illuminants were used. The degree of

visual adjustment in these directions integrate smoothly in the pattern of Ex-

periment A. Performance in the green–blue direction, for instance, is about

the same as performance in the green and in the blue direction. Such pat-

terns can also be seen at single–observer level. Thus, the irregularity of

performance along different color axes has some systematic nature. Overall,

there is best performance when illuminant changes are in greenish and bluish

directions.

Altogether, the results of the related studies from other color constancy

paradigms are consistent with the present results. Two results stand out.


First, color direction of illuminant changes plays some role for color con-

stancy. There is a predominance of performance in greenish and bluish di-

rections over yellowish and reddish directions. Second, there is evidence that

the same result patterns account for the present situation as well as for suc-

cessive color constancy situations. This becomes particularly obvious when

comparing the present results with those of Delahunt & Brainard (2004a),

for the same illuminants and a quite large number of observers were used

in both studies. The mechanisms of the two types of color constancy show

similar performance patterns across different illuminant directions.

5.3 Experiment 3: The role of color direction

under various signal–to–noise ratios

The previous experiment showed significant differences in performance along

different illuminant color directions. However, the experiment’s signal–to–

noise ratio based the surface change magnitude of 0.03 units in CIE u’v’

space, and the illuminant change magnitude of 60 CIELab ∆E∗ units, is ar-

bitrary. Considering that CIELab and CIELuv color spaces are not exactly

perceptually uniform, there is some possibility that the obtained effects re-

sult from perceptually unequal illuminant change magnitudes. If the effect

is intrinsic to the color direction of illuminant changes, the pattern of per-

formance should be similar when using different signal–to–noise ratios in the

experiment. To investigate this issue, I repeated the previous experiment,

this time increasing and decreasing the noise component in the paradigm by

altering uniform illuminant change magnitudes.


5.3.1 Methods

Observers

Three observers from Experiment 2 participated in this experiment, CA (the

author), SW, and TD. All had normal color vision as assessed by Ishihara

color plates (Ishihara, 1917). All observers, except the author (CA), were

naıve about the purpose of the experiment.


CIE D65 was used as the initial illuminant. 16 new test illuminants were

introduced. Their CIE u’v’ chromaticity coordinates were constructed to lie

in the same directions as the illuminants from Experiment 2. Eight of them

had a distance of 30 CIELab ∆E∗ units (Red30, RY30, Yellow30, YG30,

Green30, GB30, Blue30, BR30), and eight had a distance of 85 CIELab ∆E∗

units (Red85, RY85, Yellow85, YG85, Green85, GB85, Blue85, BR85) from

the D65 illuminant. Figure 5.13 shows all test illuminants along with the

test illuminants from Experiment 2 for comparison. CIE u’v’ chromaticity

coordinates of the illuminants are listed in Table 5.1. Illuminants Red30,

RY30, Yellow30, Blue30, BR30, as well as Red85, RY85, Blue85, and BR85

were constructed using daylight basis functions, YG30, Green30, GB30, as

well as Yellow85, YG85, Green85, and GB85 were constructed using monitor

basis functions. Surfaces were drawn randomly without replacement from

the pool of 226 spectral reflectances. The average luminance of the images

was held constant at 4 cd/m2, but individual surfaces varied from 0.65 to

8.81 cd/m2.


0.12 0.20 0.280.38

0.46

0.54

u’

v’

Figure 5.13: CIE u’v’ chromaticity coordinates of test illuminants. Diamonds

depict the eight illuminants which had a distance of 30 CIELab ∆E∗ units (Red30,

RY30, Yellow30, YG30, Green30, GB30, Blue30, BR30), and triangles the eight

illuminants which had a distance of 85 CIELab ∆E∗ units (Red85, RY85, Yellow85,

YG85, Green85, GB85, Blue85, BR85) from initial CIE D65 illuminant (black

square). For comparison, CIELab ∆E∗ = 60 illuminants are depicted in grey.


Procedure

The first Mondrian pattern was always illuminated by CIE D65. Within

sessions, the illuminant of the second pattern was drawn from exactly one

of four pools with four test illuminants each. The first pool consisted of

Red30, Yellow30, Green30, and Blue30, the second of RY30, YG30, GB30,

and BR30. The third and fourth pool consisted of the respective ∆E∗ = 85

illuminants. Illuminants were drawn randomly from each pool. The selection

of the pools of test illuminants were counterbalanced over sessions. Between

images, either an illuminant change or a surface change occurred randomly.

In illuminant change trials, the second Mondrian was simply illuminated

by one of the test illuminants. In the surface change condition, the same

illuminant change occurred, but additionally chromaticity coordinates of a

random quarter of the surfaces was shifted in the illuminant change direction,

a second quarter in the opposite direction, and a third and fourth quarter in

the two orthogonal directions, respectively. The magnitude of these shifts was

0.03 units in u’v’ space. There were 200 trials per session, divided into three

blocks with short intervening breaks. Each observer made 300 judgments for

each of the 16 illuminant changes.

5.3.2 Results

Figures 5.14–5.17 show discrimination performance d’ of the three observers,

as well as the mean over observers. In each figure, data is depicted in a polar

plot and a bar plot similar to Experiment 2B (Figures 5.7–5.12). In the po-

lar plots, black circles and light grey diamonds show performance under 30

∆E∗ and 85 ∆E∗ illuminant changes, respectively. For comparison, perfor-

mance under 60 ∆E∗ illuminant changes is also shown (dark grey squares).


In bar plots, plain bars and dotted bars represent performance in conditions

with illuminant change magnitudes of 30 ∆E∗ and 85 ∆E∗ units, respec-

tively. Checkered bars show results under 60 ∆E∗ illuminant changes for

comparison.

A within–subject two–way ANOVA was conducted for the three observers,

with factors illuminant color direction (Red, Red–Yellow, Yellow, Yellow–

Green, Green, Green–Blue, Blue, Blue–Red) and uniform illuminant change

magnitude (∆L∗ = 30, 60, 85). For each observer, there is a significant ef-

fect of illuminant color direction (CA: F=6.04, MSE=0.17, p<0.01; SW:

F=12.19, MSE=0.20, p<0.01; TD: F=11.99, MSE=0.12, p<0.01) and of uni-

form illuminant change magnitude (CA: F=74.16, MSE=0.10, p<0.01; SW:

F=166.20, MSE=0.11, p<0.01; TD: F=53.87, MSE=0.10, p<0.01). The in-

teraction of the factors is significant for observers CA (F=2.52, MSE=0.12,

p<0.01) and TD (F=2.37, MSE=0.22, p<0.01) and marginally significant

for SW (F=1.70, MSE=0.18, p=0.08). One–way ANOVAs for each ob-

server, separately for the two illuminant shift magnitudes ∆L∗ = 30 and

∆L∗ = 85, respectively, reveal an effect of illuminant color direction. In

the ∆L∗ = 30 condition, the effect was significant for observer SW (F=6.42,

MSE=0.17, p<0.01) and TD (F=8.68, MSE=0.14, p<0.01), and marginally

for CA (F=2.03, MSE=0.12, p=0.08). In the ∆L∗ = 85 condition, there was

a significant effect for all observers (CA: F=2.41, MSE=0.14, p=0.04, SW:

F=5.10, MSE=0.16, p<0.01, TD: F=3.48, MSE=0.18, p<0.01). To capture

possible observer differences, a re–analysis of the data was done with ob-

server as an additional factor. The three–way ANOVA was conducted with

factors observer (CA, SW, TD), illuminant direction (Red, Red–Yellow, Yel-

low, Yellow–Green, Green, Green–Blue, Blue, Blue–Red), and uniform illu-

minant change magnitude (∆L∗ = 30, 60, 85). There are significant observer


disc

rimin

atio

nin

dex

d‘

0

1

2

3

d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

d‘ = 3

YR GYG GB BRBRYilluminant direction

u‘

v‘

CA

Figure 5.14: Results for observer CA. Upper panel: Polar plot within CIE u’v’

coordinate system. The filled circle represents u’v’ coordinates of CIE D65, direc-

tion from the center represents color direction in CIE u’v’ space, and distance from

the center represents discrimination index d’. Lower panel: Bar plot for the same

data. Illuminant shift magnitude of 30 ∆E∗ units is indicated by black circles and

plain bars, and magnitude of 85∆E∗ units by light grey diamonds and dotted bars.

For comparison, data from the previous experiment with 60 ∆E∗ units (dark grey

squares and checkered bars) is reprinted. Error bars show ± 1 SEM.


disc

rimin

atio

nin

dex

d‘

0

1

2

3

YR GYG GB BRBRY

d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

d‘ = 3


u‘

v‘

SW

Figure 5.15: Results for observer SW. Polar plot within CIE u’v’ coordinate

system. The filled circle represents u’v’ coordinates of CIE D65, direction from

the center represents color direction in CIE u’v’ space, and distance from the

center represents discrimination index d’. Lower panel: Bar plot for the same






disc

rimin

atio

nin

dex

d‘

0

1

2

3

YR GYG GB BRBRY

d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

d‘ = 3


u‘

v‘

TD

Figure 5.16: Results for observer TD. Polar plot within CIE u’v’ coordinate









d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

d‘ = 3

disc

rimin

atio

nin

dex

d‘

YR GYG GB BRBRY0

1

2

3


u‘

v‘

mean

Figure 5.17: Mean results over observers. Polar plot within CIE u’v’ coordinate









differences (F=45.41, MSE=0.10, p<0.01) along with significant effects of

illuminant direction (F=10.42, MSE=0.19, p<0.01), and uniform illuminant

change magnitude (F=246.15, MSE=0.12, p<0.01). There is also a high in-

teraction of observer and illuminant direction (F=9.71, MSE=0.15, p<0.01)

and of illuminant change magnitude and illuminant direction (F=3.02, MSE=0.13,

p=0.01). For a better insight, Figure 5.18 replots data of Figure 5.17 and

shows differences in mean discrimination performance over observers under

illuminant change magnitudes ∆L∗ = 30 and ∆L∗ = 85. It is evident that

delta

d‘

YR GYG GB BRBRY0

1

2

3

d‘ = 1

d‘ = 2

R

YGY

RY

B

GB

G

BR

subject CA d‘ = 3


Figure 5.18: Differences between performances in 30 ∆E∗ and 85 ∆E∗ conditions

over observers. Error bars show ± 1 SEM.

performance differences are quite similar across illuminant directions. This

shows that performance patterns for these two magnitudes are approximately

equal.


5.3.3 Discussion

The purpose of the experiment was to investigate if the performance pattern

from Experiment 2 depends solely on non–linearities of color space or if it is

intrinsic to color direction of illuminant changes. If the latter was true, the

pattern should remain stable across changes in illuminant change magnitude,

i. e. across changes in signal–to–noise ratios in this paradigm. It was shown

that within subjects there was some variation in the performance patterns

over different illuminant shift magnitudes. However, these variations have

no systematic nature. This is particularly evident from mean results over

observers. Result patterns from 30 ∆E∗ and 85 ∆E∗ conditions are rather

similar. However, compared to the pattern of the 60 ∆E∗ condition the

effect of illuminant direction is slightly reduced. This may result from certain

floor and ceiling effects in these conditions. Particularly, performance in the

green and green–blue direction deteriorates to some extent. Performance

in the blue direction, on the other hand, is highest in all three conditions

and performance in the red direction is always rather low. Overall, the

pattern remained rather stable under changes in signal–to–noise ratios in the

experiment. There is evidence now, that, in this discrimination paradigm,

the effect of color direction in illuminant changes on the degree of color

constancy is not due to perceptual non–linearities of color space, but is an

attribute of the visual system.


5.4 Experiment 4: The role of surface collec-

tion in illuminant changes

A color constant visual system is able to maintain object colors despite

changes in surrounding illumination. Since we encounter different environ-

ments in everyday life, this feature must hold across a variety of scenes. In

section 3.1, we made a distinction between urban scenes, where spectral re-

flectances are rather equally distributed in color space with mean chromatic-

ities clustering along the daylight locus, and rural scenes, where reflectances

are distributed more in the green area, with means lying to the green side of

the daylight locus. By far the fewest reflectances fall to the red side of the

daylight locus. From our daily experience, our visual system compensates

well for illuminant changes mostly independent of scene surface composition.

However, it has been shown in Experiments 2 and 3 that there are also ir-

regularities in color constancy under illuminant changes with different color

directions which are hardly recognized in everyday life. Therefore, there is

some possibility that surface collection also influences the degree of visual

adjustment to an illuminant.

There is some research on this issue in successive color constancy sit-

uations. Bauml (1994, 1999b) found some differences in observers’ settings

under different surface collections with diverse mean chromaticities. Brainard

(1998) used differently colored backgrounds and found differences in achro-

matic loci. However, when surface collections differ mainly in luminance,

rather than in mean chromaticity, no such effect can be found (Bauml, 1995).

Furthermore, in the studies of Bauml (1994, 1995), slight observer differences

were found. Bauml (1999a) investigated appearance and surface color in si-

multaneous situations. He found almost no differences between color matches


when collections differed only in luminance, but found some when collections

differed in mean chromaticity. He also found a slight interaction of illuminant

direction and surface collection in both conditions.

There is no color constancy research investigating a possible influence of

surface collection in situations where illumination changes temporally and

rapidly. It is also unclear whether there is an interaction of surface collec-

tion and color direction of illuminant change. It is the purpose of the next

experiment to fill this gap. Two possible outcomes can be expected. First,

Experiment 2 showed that the amount of visual adjustment is related to the

distribution of illuminants in our natural environment. If degrees of color

constancy are also related to the distribution of surfaces in our environment,

then a pattern should show up with high constancy under green, medium

under yellow and blue, and low constancy under red collections. Second, if

the visual system processes illuminants and surfaces separately, and the de-

gree of color constancy only depends on the color direction of the illuminant

change, then the amount of visual adjustment should be similar under each

surface collection.

5.4.1 Methods

Observers

Four observers participated in this experiment, AW, BD, CA (the author),

and HM. All had normal color vision as assessed by Ishihara color plates

(Ishihara, 1917). All observers except the author (CA) were naıve about the

purpose of the experiment.



As experimental illuminants, Blue60 and Red60 (Figure 5.5, Table 5.1) from

Experiment 2 were chosen. As experimental surfaces, the whole set of 226

reflectances was split into four slightly overlapping subsets (Figure 5.19) to

obtain surface collections containing mainly red, yellow, green, and blue sur-

faces. Each collection contained 61 different surfaces. As a fifth collection,

the whole set of 226 surfaces was used (Figure 4.1). It served as a neutral col-

lection. The average luminance of the images was held constant at 4 cd/m2,

but individual surfaces varied from 0.65 to 8.81 cd/m2.

Procedure

The first Mondrian pattern was always illuminated by CIE D65. The illu-

minant of the second pattern was either test illuminant Blue60 or Red60.

Between images, either an illuminant change or a surface change occurred

randomly. In illuminant change trials, the second Mondrian was simply illu-

minated by one of the test illuminants. In the surface change condition, the

same illuminant change occurred, but additionally chromaticity coordinates

of a random quarter of the surfaces were then shifted along the Blue axis,

a second quarter along the Yellow axis, a third quarter along the Red axis,

and a fourth along the Green axis. The magnitude of these shifts was 0.03

units in CIE u’v’ space. The surfaces which the Mondrian patterns were

composed of were drawn randomly, without replacement, from one of the

five surface collections, also chosen randomly for each trial. There were 250

trials per session, divided into three blocks with short intervening breaks.

Within sessions, only one of the test illuminants was used.


0.14 0.255 0.370.31

0.425

0.54

v'

u'

0.14 0.255 0.370.31

0.425

0.54

v'

u'0.14 0.255 0.37

0.31

0.425

0.54

v'

u'

0.14 0.255 0.370.31

0.425

0.54

v'

u'

0.14 0.255 0.370.31

0.425

0.54

v'

u'

Figure 5.19: Experimental surface collections. In each panel, the CIE u’v’ coor-

dinates of a single collection (Red, Yellow, Green, Blue), illuminated by D65 (open

square), are depicted in the respective color. For comparison, coordinates of the

remainder of the entire surface set is shown in light grey in each panel.


5.4.2 Results

Figure 5.20 shows discrimination performance d’ for observers AW, BD, and

CA, and Figure 5.21 for observer HM, as well as mean results over observers,

and results collapsed over observers and illuminant directions.

A two-way ANOVA with factors illuminant direction (Blue, Red) and sur-

face collection (Neutral, Red, Yellow, Green, Blue) shows, for each of the four

observers, effects of illuminant direction and surface collection. The effect

of illuminant direction is significant for observer AW (F=95.91, MSE=0.16,

p<0.01), BD (F=11.03, MSE=0.18, p=0.02), and CA (F=7.40, MSE=0.17,

p=0.04), but not for HM (F=3.11, MSE=0.16, p=0.14). For each observer,

overall performance is higher in the blue direction than in the red direc-

tion. There is also a significant effect of surface collection for observer AW

(F=23.75, MSE=0.23, p<0.01), BD (F=38.11, MSE=0.27, p<0.01), and HM

(F=6.82, MSE=0.40, p<0.01), and marginally for CA (F=2.34, MSE=0.08,

p=0.09). Observers BD and CA have highest overall performance under the

green collection, and observers AW and HM under the green and blue col-

lection. Results under the neutral surface collection are directly comparable

to Experiment 2A on the role of illuminant direction (Figure 5.6). Observer

CA participated in both experiments and replicated his results. There is a

significant interaction of illuminant direction and surface collection for all

four observers (AW: F=2.93, MSE=0.27, p=0.05; BD: F=11.73, MSE=0.23,

p<0.01; CA: F=7.04, MSE=0.17, p<0.01; HM: F=3.90, MSE=0.30, p=0.02).

Figures 5.20 and 5.21 show, for each observer, a rather stable performance

under the green and blue collections across illuminant changes. However,

performance under the neutral, red, and yellow collections deteriorates for

each observer when illuminant direction is changed from blue to red.


3

2

1

0

3

2

1

0

3

2

1

0N R Y G B N R Y G B

Blue Red

AW

BD

CA

discriminationindexd‘



Figure 5.20: Results for observers AW, BD, and CA. In each panel the two bar

groups show performance in illuminant directions Blue and Red. Within each

bar group, performance under the five surface collections (Neutral, Red, Yellow,

Green, Blue) is shown. Error bars show ± 1 SEM.


3

2

1

0

3

2

1

0

3

2

1

0

N R Y G B N R Y G B

Blue Red

N R Y G B

HM

Mean




surface collection

Figure 5.21: Results for observer HM (upper panel), depicted as in Figure 5.20,

results for data collapsed over observers (middle panel), and for data collapsed

over both observers and illuminant directions (bottom panel). Error bars show ±

1 SEM.


The middle panel of Figure 5.21 shows mean performance collapsed over

observers where this effect becomes particularly obvious. Performances un-

der the neutral collection again replicated results from Experiment 2 (Figure

5.6, lower right panel). To capture the effect of observer differences, data

was re-analyzed with a 3-way ANOVA with factors observer (AW, BD, CA,

HM), illuminant direction (Blue, Red), and surface collection (Neutral, Red,

Yellow, Green, Blue). Besides the expected effects of illuminant direction

(F=88.61, MSE=0.15, p<0.01) and surface collection (F=44.10, MSE=0.22,

p<0.01), there are again significant observer differences (F=7.62, MSE=0.28,

p<0.01). The significant interaction of illuminant direction and surface col-

lection (F=17.69, MSE=0.23, p<0.01) confirms the visual examination of

Figure 5.21 (middle panel). A significant interaction of illuminant direc-

tion and observer, already found in Experiments 2 and 3, is also found here

(F=12.45, MSE=0.17, p<0.01), along with a significant variation of surface

collection with observer (F=11.82, MSE=0.25, p<0.01).

The lower panel of Figure 5.21 shows results of the same data collapsed

over observers and illuminant directions. The declining order of performance

under surface collection is Green, Blue, Yellow, Neutral, and Red. The pat-

tern looks rather similar to the pattern obtained for respective illuminant

directions in Experiment 2 (Figure 5.6, lower right panel). For instance, per-

formance is high under the green surface collection, as well as in the green

illuminant direction, and performance is rather low under the red collection,

as well as in the red illuminant direction. A two-way ANOVA with factors

observer (AW, BD, CA, HM) and surface collection (Neutral, Red, Yellow,

Green, Blue) confirms the effect of surface collection (F=17.22, MSE=0.57,

p<0.01), besides effects of observer (F=5.32, MSE=0.41, p=0.04) and a sig-

nificant interaction of the factors (F=19.58, MSE=0.28, p<0.01).


Table 5.4: False Alarm rates across test illuminants (Blue, Red) and across sur-

face collections (N=Neutral, R=Red, Y=Yellow, G=Green, B=Blue) of Experi-

ment 3 for individual observers as well as for the mean under each test illuminant.

The overall mean is calculated by collapsing data over both observers and test

illuminants.

Observer Blue-N Blue-R Blue-Y Blue-G Blue-BAW 0.59 0.39 0.13 0.07 0.07BD 0.19 0.02 0.45 0.02 0.02CA 0.44 0.03 0.08 0.16 0.02HM 0.62 0.03 0.16 0.35 0.02mean Blue 0.46 0.12 0.21 0.15 0.03

Observer Red-N Red-R Red-Y Red-G Red-BAW 0.86 0.44 0.80 0.09 0.14BD 0.70 0.02 0.11 0.04 0.03CA 0.46 0.11 0.49 0.03 0.04HM 0.72 0.73 0.73 0.22 0.28mean Red 0.69 0.33 0.53 0.09 0.12

overall mean 0.57 0.22 0.37 0.12 0.08

Table 5.4 lists False Alarm rates of individual observers the mean to

investigate whether they vary across condition and correlate somehow with

discrimination performance. It can be clearly seen that False Alarm rates

vary widely across surface collections but do not correlate with discrimination

indices. For instance, observer BD under the blue illuminant has rather

similar discrimination performance of about 1.3 under the neutral and yellow

collection but rather different False Alarm rates of 0.19 and 0.45. In turn,

False Alarm rates of 0.02 both under the red and green collection do not

correlate with rather different discrimination indices of about 0.9 and 3.2.


5.4.3 Discussion

This experiment was designed to investigate the role of surface collection on

the degree of surface color constancy in situations with rapid, temporal il-

luminant changes. Observers could reliably discriminate illuminant changes

from surface changes in a variety of scenes and illuminants. An effect of

illuminant direction was found with better performance in the blue direction

than in the red direction. This result is consistent with findings earlier in

this work (Experiments 2 and 3). There was also an effect of surface col-

lection on performance. This effect varied somewhat between observers and

interacted with illuminant direction. When data is collapsed over observers,

this interaction becomes particularly apparent. While performance under

green and blue collections remains quite stable, performance under the other

collections deteriorate when illuminant direction changes from Blue to Red.

When data is further collapsed over illuminant directions, a decline of per-

formance under different surface collections can be observed, the order being

Green, Blue, Yellow, Neutral, Red. This pattern reminds of results previ-

ously found in this work (Experiment 2), where performance under different

illuminant directions was quite similar, with performance being highest in

green and blue directions, mediocre in the yellow direction, and low in the

red direction. There seems to be some evidence that the visual system, re-

garding the degree of color constancy, adjusts to the light incident at the eye,

i. e. the product of illuminant and surface properties. For instance, color

constancy under a neutral surface collection when illuminant changes in the

blue direction is comparable to constancy under a blue surface collection

when illuminant changes in blue, red and probably other color directions.

It was investigated whether False Alarm rates vary across conditions and


correlate with discrimination performance. It could be shown that, indeed,

False Alarm rates vary widely across surface collections. However, they do

not correlate with discrimination performance. The same result was obtained

in Experiment 2 for varying illuminant directions. False Alarm rates, there-

fore, do not predict differences in discrimination performance under changing

illuminant directions and surface collections.

When relating these results to findings from studies concerning succes-

sive and simultaneous color constancy situations using similar illuminants

and surface collections, some similarities become apparent. Better perfor-

mance under the blue than the red illuminant was also found by Delahunt

& Brainard (2004a, 2004b). Some effect of surface collection, when varied

in mean chromaticity, was also found by Bauml (1994, 1995, 1999b, 1999a)

and Brainard (1998). However, Bauml (1995) did not find this effect when

varying the surface collection mainly in luminance rather than chromaticity.

In Experiment 1 of this work, it was shown that luminance of an illuminant

does not have a major impact on discrimination performance. These two

findings support the assumption that the visual system adjusts to the prod-

uct of illumination and surface reflectance, rather than separately (but see

Bauml (1994) for strong effects of surface collection which are separable from

effects of illumination). Slight effects of surface collection and an interaction

were also found by Bauml (1999b, 1999a) and Brainard (1998).

Different degrees of constancy under different surface collections can be

related to the distribution of surfaces in our environment. As mentioned

above, mean chromaticities of urban surface collections lie near the daylight

locus (Nascimento et al., 2002). However, chromaticities of rural surface

collections lie on average to the green side of the daylight locus (e. g. Webster

& Mollon, 1997; Nascimento et al., 2002). In addition, reddish surfaces are


relatively rare in rural environments. Based on these data, color constancy

performance under a particular surface collection correlates somehow with

the frequency of those surfaces in rural environments.

The close entanglement of the roles of illuminant direction and surface

collection on the degree of color constancy on the one hand, and correlation

of color constancy and frequency of surfaces in natural environments on the

other hand, is not surprising when we consider how non-daylight illumination

arises. It is the product of the surface reflectance and the impinging light on

this surface. As a conclusion the frequency of colors of indirect illuminations

correlate with the colors of surfaces by which they arise. Reddish illuminants,

for instance, are rather rare because reddish surfaces are rather rare in natural

environments.

Chapter 6

General Discussion

Summary of results

In this chapter, a series of four experiments was run to systematically inves-

tigate the role of color direction of illuminant changes and surface collection

on the degree of color constancy in situations with rapid temporal illuminant

changes. In Experiment 1, the experimental setup was evaluated. It was

found that luminance in illuminant changes only plays a minor role for the

degree of color constancy. In Experiment 2, it was found that the degree of

color constancy depends on the color direction of illuminant changes. Best

performance was in greenish and blueish directions, and worst performance

in reddish directions. In Experiment 3, different illuminant change magni-

tudes were tested to reassess the performance pattern obtained and exclude

the possibility that the irregularities found are due to non–linearities of color

space. As a result, the overall pattern stayed rather stable across illuminant

change magnitudes. In Experiment 4, the role of surface collection for color

constancy was investigated. Performance was highest under the green col-

108

CHAPTER 6. GENERAL DISCUSSION 109

lection, and deteriorated under the other collections blue, yellow, and red in

declining order. Furthermore, there was an interaction of illuminant direction

and surface collection.

The role of illuminants and surface collections

The motivation of this study was to investigate the roles of illuminant color

direction and surface collection on the degree of color constancy under rapid

temporal illuminant changes. For this purpose, the paradigm of Craven &

Foster (1992) was applied, in which observers had to discriminate changes

in illuminant from changes in surfaces within a scene. It is shown that

the degree of color constancy in situations with rapid temporal illuminant

changes depends on the color direction of these illuminant changes. This

is true for changes of chromaticity, but not for changes in luminance which

has almost no effect on color constancy. Overall, performance was best for

greenish and bluish color directions, medium for yellowish directions, and

worst for reddish directions. The surface collection also plays some role on

the degree of simultaneous color constancy. The results resemble the pattern

for the effect of illuminant direction. Performance was best for the collection

with on average green reflectances, medium for collections with on average

blue and yellow reflectances, and worst for the collection consisting of on

average red reflectances. However, the effect varied somehow with illuminant

direction indicating an interaction of the two effects.

Two conclusions can be drawn from the experiments provided in this

work. First, the visual system shows color constancy in situations with rapid

temporal illuminant changes. This holds true, however to different extents,

for a considerable range of daylight and non–daylight illuminants and several


color–biased scene compositions. This type of color constancy is important

for everyday life, since we frequently encounter situations where the illumi-

nant changes rather rapidly, e. g. when an additional light source is switched

on or when the sun gets screened by a cloud. Second, the degree of color

constancy in the present paradigm seems to depend on the combination of

illuminant direction and surface collection, so the visual system seems to

adjust to some product of the two.

Relation to successive and simultaneous color

constancy

Previous color constancy research focussed on successive and simultaneous

color constancy situations. In successive situations, illumination changes

rather slowly. It is common belief by now that visual adjustment is medi-

ated by some adaptational process at receptor site in this situation (Kaiser

& Boynton, 1996). In simultaneous color constancy paradigms, where illumi-

nation changes spatially, those adaptational processes are to a large extent

excluded. Nonetheless, even when observers are asked to make surface color

matches, the visual system adjusts in terms of receptor signal scaling very

similar to adaptational processes, suggesting a close relation of apparent

color and surface color mechanisms (Bauml, 1999a). In this sense, there is a

connection between successive and simultaneous color constancy situations.

This work provides a third paradigm derived from Craven & Foster (1992),

where illumination changes rapidly in a temporal manner. All results ob-

tained in this work are consistent with or can easily be embedded in findings

from studies concerning successive and simultaneous color constancy. In


successive color constancy situations, for instance, Brainard (1998) found a

slight effect of illuminant direction. Lucassen & Walraven (1996) found bet-

ter constancy in the blue illuminant direction than in the yellow direction.

Delahunt & Brainard (2004a, 2004b) found best performance in green and

blue directions, medium performance in the yellow direction, and worst per-

formance in the red direction. Regarding the role of surface collection in

successive color constancy situations, an effect was found for collections with

rather different mean chromaticity coordinates (Bauml, 1994, 1999b), but

no effect for collections differing mainly in mean luminance (Bauml, 1995).

Brainard (1998) also found small differences in adjustment for differently col-

ored backgrounds. Overall, the results of this work are consistent with the

results of the studies concerning successive color constancy. Bauml (1999a)

found an effect for surface collections with varying chromaticity, but no effect

for collections with varying luminance only in a simultaneous color matching

paradigm. The results of this work also show an effect of surface collection

with varying mean chromaticity. He also showed that observers’ appearance

and surface color matches are similar in a qualitative way suggesting sim-

ilar constancy patterns along different color directions, and under different

surface collections in successive color constancy and in simultaneous color

constancy situations. In addition, he found a slight interaction of illuminant

direction and surface collection in both apparent and surface color situations.

An interaction was found in the present study as well. As a conclusion, this

paradigm is also related to simultaneous color constancy.

Despite reflecting rather different situations, all three paradigms seem to

be related with respect to which results they produce. However, in contrast

to this paradigm, the settings produced by matching paradigms, which are

used for successive and simultaneous color constancy experiments, provide


additional information about the way of visual adjustment. It was shown

that simple von Kries and illuminant linearity models fitted on those data

describe the characteristics of visual adjustment rather well. Moreover, these

models are rather robust against influences of illuminant direction and sur-

face collection. This leads indeed to detectable but small effects. The data

analysis of the paradigm used here involves paired comparison and appears

like a magnifying lens on the effects of illuminant direction and surface col-

lection for these model data. Therefore, it provides a detailed view on the

influence of these two factors.

Individual observer differences

In the present study, some observer differences were found. For instance,

when different illuminant directions were tested, some observers had better

performance under the yellow illuminant than under the red illuminant and

vice versa. Differences could also be observed when testing color constancy

under different surface collections. It is not easy to explain this effect. When

the role of illuminant direction and surface collection was investigated using

successive and simultaneous color matching paradigms, observer differences

were found as well (e. g. Delahunt, 2001; Bauml, 1999a). However, many

studies focussed on the characteristics of visual adjustment by fitting rather

robust models to the data, so that effects of illuminant direction and surface

collection were often small and could have been neglected for this purpose.

For this reason, observer differences were not large enough to be focussed

on. On the other hand, it is obviously important to involve far more than

just two or three or five observers in experiments to obtain reliable results

on individual differences, when the issue of illuminant direction and surface


collection is supposed to be examined. However, such a detailed analysis of

observer differences is beyond the scope of this work.

Why does color constancy depend on illumi-

nant color direction and surface collection?

This work shows that the degree of color constancy depends on the color

direction of the illuminant change and on the color bias of the scene com-

position. How can these effects be explained? The reason why performance

is better under the blue than under the yellow illuminant might be due to

the probability of daylight changes in everyday environment. In this work,

CIE D65 was used as the standard illuminant which is regarded as neutral

in color and typical for a mixture of sunlight and scattered skylight. In our

natural environment, rapid illuminant changes to the blue side of D65 occur

frequently when the sun gets shaded by a cloud. Changes to the yellow side

occur only during rather brief periods at dusk and dawn. The visual sys-

tem might adjust better to blue illuminant changes because it is more often

confronted with these kind of changes (Delahunt, 2001).

An explanation of the rather high performance in the green illuminant

direction, especially compared to that in the red direction, may be provided

by an evolutionary approach. It has been shown that in forested areas almost

the entire illumination is, due to mutual reflections, shifted towards green to

yellow–green (Endler, 1993). Given that our visual system has evolved in

such environments, this comparatively high degree of color constancy is not

surprising. Moreover, the visual system seems to have developed towards

certain goals. Old World primates, which are one of the few mammals to


have trichromatic color vision similar to that of humans, live in environ-

ments where some vital tasks are to be fulfilled in order to ensure survival of

the species. One of such tasks is to identify edible fruit against green foliage

(Allen, 1879). Osorio & Vorobyev (1996) showed empirically that trichro-

macy is superior to dichromacy in such a task. Regan, Julliott, Simmen,

Vinot, Charles–Dominique, & Mollon (2001) found that the responsivity

functions of the photoreceptors in trichromatic primates are well–matched

to succeed in this task. Another task is to discriminate emotional states,

socio–sexual signals and threat displays of conspecifics. Changizi, Zhang, &

Shimojo (2006) showed that sensitivities of medium– and long–wavelength

receptors in trichromatic primates are optimized to accomplish this task.

These studies focus at the characteristics of photoreceptors and found ev-

idence that they evolved towards accomplishing certain vital tasks in the

environment. Color constancy mechanisms, which facilitate perceiving con-

stant object colors, might as well have evolved adjusting to certain environ-

mental conditions, like living in forest areas illuminated by mostly greenish

light. However, forested areas nowadays do not have such a high significance

for humans anymore. The high performance in the blue and in the green

direction may stem from lifetime and evolutionary experiences, respectively.

However, these types of experience are entwined and it is speculative from

which source of experience in detail the present results arise.

The second factor which influences the degree of color constancy in the

present work is the surface collection. Roughly similar to the effect of illu-

minant direction, performance is best under the green surface collection and

worst under the red collection. It was mentioned in chapter 3 that mean re-

flectances of urban scenes cluster roughly along the daylight locus, whereas

mean reflectances of rural scenes are shifted towards the yellow–green area


(Nascimento et al., 2002; Hendley & Hecht, 1949). By far the least re-

flectances can be found in the red area. Again, the results obtained here

may be explained by an evolutionary approach. This parallel is not surpris-

ing since non–daylight illuminants, like green, arise from mutual reflections

on mainly greenish surfaces. This fact implies that the frequency of illumi-

nant colors correlates somehow with the occurrence of surface colors within

a scene. For instance, very few surfaces are reddish in forests, so reddish

illumination is also rather rare.

Perspectives

Effects of illuminant color direction and surface collection were found in the

present discrimination paradigm, but in appearance and surface color match-

ing paradigms as well. However, the size and the meaningfulness of these

effects depend on the issue to be investigated. When discrimination perfor-

mance is compared, as done in this work, the effects are obvious. When it

is the main interest to examine the characteristics of visual adjustment by

fitting models to data, the effects are less obvious and to first approximation

may even be neglected. Therefore, models of color constancy, like illuminant

linearity, seem to be very robust against such effects. These models are very

simple and, anyway, provide a good description of how the visual system

adjusts to illuminant changes. Illuminant linearity states that receptor scal-

ings resulting from an illuminant change depend linearly on this change. If

illuminant linearity holds, then, in a matching paradigm, color matches for

two different illuminant changes provide data to predict the match for any

third illuminant change that is a linear combination of the two. This seems

plausible under the assumption that the amount of visual adjustment is equal


under all illuminant changes. This work shows, however, that this is not the

case. If the degree of color constancy under two different illuminants, say a

red and a blue one, is rather different then the prediction of a match under

a blue-red illuminant might be bad. It would be interesting to examine the

effects of illuminant direction on the illuminant linearity model in detail. De-

pending on the size of the influence, a decision should be made whether the

effects should be incorporated into existing models. This may be a challenge

for future research.

Matching paradigms and the operational discrimination paradigm are

rather different approaches to the issue of color constancy, and each one has

pros and cons. Matching paradigms produce more information, especially for

evaluating models for visual adjustment as described above, since matches are

made in a two– or three–dimensional color space. However, matching tasks

are rather time–consuming and demand adjustment of a color by operating

sliders or the like. This is a very unnatural procedure which is hardly related

to any task regarding color judgment in our daily life, and therefore requires

some time for training. Discrimination tasks, in turn, seem rather natural

for they have to be accomplished in everyday life. When colors of a scene

change, one has to judge whether this is due to a change in illuminant or

to a change in objects. Furthermore, discrimination tasks have shown to

be rather easy for observers to accomplish, and require, if at all, only a

few minutes of training. As shown in this work, a discrimination paradigm

provides a detailed view on differences in visual adjustment depending on

illuminant direction or surface collection. However, the information one gets

from a discrimination paradigm is very limited. It is not possible to explain

the characteristics of visual adjustment processes as it is possible with data

from matching paradigms.


Both matching and discrimination paradigms provide information which

contribute to the understanding of color constancy. As described above, they

are able to benefit from each other. Therefore, it is necessary to consider

results from both paradigms and integrate them to expand the view on the

phenomenon of color constancy.

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Appendix A

This Appendix consists of one table and three figures. Table A1 lists CIE

u’v’ chromaticity coordinates of the 226 experimental surfaces and the sur-

face collection to which each individual surface belonged. Figures A1 and

A2 show, respectively, the daylight and monitor basis functions used for

modelling experimental illuminants. Figure A3 shows the reflectance basis

functions used for modelling experimental surfaces.

Table A1: All 226 experimental surfaces. CIE u’v’ chromaticity coordinates ofsurfaces illuminated by CIE D65 as well as membership to surface collections arelisted.

Surface collections

Surface u’ v’ Collection

1 0,197 0,468 Neutral2 0,199 0,466 Neutral3 0,198 0,465 Neutral4 0,197 0,466 Neutral5 0,197 0,467 Neutral6 0,198 0,469 Neutral7 0,197 0,468 Neutral8 0,244 0,471 Neutral9 0,237 0,476 Neutral

10 0,231 0,476 Yellow, Neutral11 0,227 0,474 Yellow, Neutral12 0,217 0,473 Yellow, Neutral13 0,277 0,475 Yellow, Neutral14 0,280 0,485 Yellow, Neutral15 0,263 0,479 Yellow, Neutral16 0,259 0,481 Yellow, Neutral17 0,292 0,474 Yellow, Neutral18 0,302 0,485 Yellow, Neutral19 0,294 0,486 Yellow, Neutral20 0,289 0,485 Yellow, Neutral21 0,331 0,492 Yellow, Neutral22 0,329 0,493 Yellow, Neutral23 0,352 0,495 Yellow, Neutral24 0,351 0,494 Yellow, Neutral25 0,252 0,483 Yellow, Neutral26 0,272 0,496 Yellow, Neutral27 0,264 0,498 Yellow, Neutral28 0,256 0,493 Yellow, Neutral29 0,238 0,487 Yellow, Neutral30 0,292 0,502 Yellow, Neutral31 0,296 0,508 Yellow, Neutral32 0,283 0,505 Yellow, Neutral33 0,229 0,487 Yellow, Neutral

129

APPENDIX A 130


34 0,232 0,492 Yellow, Neutral35 0,234 0,493 Yellow, Neutral36 0,230 0,490 Yellow, Neutral37 0,221 0,485 Yellow, Neutral38 0,216 0,483 Yellow, Neutral39 0,261 0,509 Yellow, Neutral40 0,256 0,512 Yellow, Neutral41 0,249 0,504 Yellow, Neutral42 0,235 0,495 Yellow, Neutral43 0,223 0,492 Yellow, Neutral44 0,232 0,507 Yellow, Neutral45 0,234 0,513 Yellow, Neutral46 0,225 0,508 Yellow, Neutral47 0,207 0,492 Yellow, Neutral48 0,206 0,490 Yellow, Neutral49 0,207 0,495 Yellow, Neutral50 0,207 0,492 Yellow, Neutral51 0,206 0,489 Yellow, Neutral52 0,204 0,486 Yellow, Neutral53 0,216 0,513 Yellow, Neutral54 0,200 0,496 Yellow, Neutral55 0,199 0,499 Green, Yellow, Neutral56 0,204 0,516 Green, Yellow, Neutral57 0,200 0,508 Green, Yellow, Neutral58 0,187 0,497 Green, Yellow, Neutral59 0,193 0,496 Green, Yellow, Neutral60 0,192 0,492 Green, Yellow, Neutral61 0,193 0,492 Green, Yellow, Neutral62 0,194 0,488 Green, Yellow, Neutral63 0,194 0,486 Green, Yellow, Neutral64 0,189 0,507 Green, Yellow, Neutral65 0,188 0,512 Green, Yellow, Neutral66 0,189 0,517 Green, Yellow, Neutral67 0,190 0,511 Green, Yellow, Neutral68 0,191 0,505 Green, Yellow, Neutral69 0,176 0,495 Green, Yellow, Neutral70 0,158 0,514 Green, Yellow, Neutral71 0,165 0,503 Green, Yellow, Neutral72 0,171 0,504 Green, Yellow, Neutral73 0,170 0,499 Green, Yellow, Neutral74 0,177 0,497 Green, Yellow, Neutral75 0,180 0,495 Green, Yellow, Neutral76 0,157 0,526 Green, Yellow, Neutral77 0,161 0,518 Green, Yellow, Neutral78 0,166 0,511 Green, Yellow, Neutral79 0,176 0,504 Green, Yellow, Neutral80 0,160 0,527 Green, Yellow, Neutral81 0,160 0,524 Green, Yellow, Neutral82 0,167 0,482 Green, Yellow, Neutral83 0,173 0,479 Green, Yellow, Neutral84 0,176 0,477 Green, Yellow, Neutral85 0,177 0,478 Green, Yellow, Neutral86 0,182 0,476 Green, Yellow, Neutral87 0,183 0,479 Green, Yellow, Neutral88 0,162 0,487 Green, Yellow, Neutral89 0,167 0,485 Green, Yellow, Neutral90 0,176 0,481 Green, Yellow, Neutral91 0,166 0,486 Green, Yellow, Neutral92 0,169 0,478 Green, Yellow, Neutral93 0,169 0,465 Green, Yellow, Neutral94 0,172 0,467 Green, Yellow, Neutral95 0,177 0,469 Blue, Green, Neutral96 0,180 0,472 Blue, Green, Neutral97 0,163 0,467 Blue, Green, Neutral98 0,172 0,470 Blue, Green, Neutral99 0,164 0,457 Blue, Green, Neutral

100 0,170 0,459 Blue, Green, Neutral101 0,169 0,442 Blue, Green, Neutral102 0,172 0,449 Blue, Green, Neutral103 0,176 0,452 Blue, Green, Neutral104 0,179 0,453 Blue, Green, Neutral105 0,183 0,462 Blue, Green, Neutral106 0,167 0,444 Blue, Green, Neutral107 0,173 0,454 Blue, Green, Neutral108 0,179 0,460 Blue, Green, Neutral109 0,167 0,449 Blue, Green, Neutral110 0,169 0,428 Blue, Green, Neutral111 0,170 0,433 Blue, Green, Neutral112 0,173 0,440 Blue, Green, Neutral113 0,177 0,447 Blue, Green, Neutral114 0,169 0,438 Blue, Green, Neutral115 0,179 0,421 Blue, Green, Neutral116 0,185 0,435 Blue, Neutral117 0,187 0,442 Blue, Neutral118 0,187 0,443 Blue, Neutral119 0,189 0,448 Blue, Neutral120 0,188 0,453 Blue, Neutral121 0,176 0,410 Blue, Neutral122 0,179 0,423 Blue, Neutral123 0,181 0,430 Blue, Neutral124 0,183 0,438 Blue, Neutral125 0,184 0,443 Blue, Neutral126 0,168 0,389 Blue, Neutral127 0,171 0,405 Blue, Neutral128 0,174 0,417 Blue, Neutral129 0,179 0,424 Blue, Neutral130 0,181 0,436 Blue, Neutral131 0,167 0,403 Blue, Neutral132 0,174 0,422 Blue, Neutral133 0,200 0,385 Blue, Neutral134 0,201 0,399 Blue, Neutral135 0,199 0,419 Blue, Neutral136 0,198 0,426 Blue, Neutral

APPENDIX A 131


137 0,198 0,435 Blue, Neutral138 0,197 0,446 Blue, Neutral139 0,203 0,379 Blue, Neutral140 0,202 0,383 Blue, Neutral141 0,197 0,398 Blue, Neutral142 0,195 0,411 Blue, Neutral143 0,197 0,423 Blue, Neutral144 0,196 0,436 Blue, Neutral145 0,201 0,368 Blue, Neutral146 0,196 0,380 Blue, Neutral147 0,195 0,396 Blue, Neutral148 0,198 0,410 Blue, Neutral149 0,201 0,324 Blue, Neutral150 0,198 0,367 Blue, Neutral151 0,195 0,384 Blue, Neutral152 0,218 0,422 Blue, Neutral153 0,210 0,440 Blue, Neutral154 0,206 0,446 Blue, Neutral155 0,204 0,449 Blue, Neutral156 0,203 0,451 Neutral157 0,202 0,454 Neutral158 0,223 0,399 Neutral159 0,220 0,412 Neutral160 0,214 0,430 Red, Neutral161 0,210 0,433 Red, Neutral162 0,206 0,439 Red, Neutral163 0,234 0,370 Red, Neutral164 0,226 0,393 Red, Neutral165 0,220 0,413 Red, Neutral166 0,216 0,419 Red, Neutral167 0,211 0,426 Red, Neutral168 0,234 0,376 Red, Neutral169 0,226 0,396 Red, Neutral170 0,220 0,406 Red, Neutral171 0,216 0,415 Red, Neutral172 0,244 0,350 Red, Neutral173 0,234 0,386 Red, Neutral174 0,226 0,390 Red, Neutral175 0,244 0,363 Red, Neutral176 0,244 0,401 Red, Neutral177 0,239 0,427 Red, Neutral178 0,230 0,441 Red, Neutral179 0,228 0,447 Red, Neutral180 0,218 0,452 Red, Neutral181 0,256 0,386 Red, Neutral182 0,247 0,408 Red, Neutral183 0,244 0,429 Red, Neutral184 0,239 0,439 Red, Neutral185 0,224 0,444 Red, Neutral186 0,267 0,394 Red, Neutral187 0,255 0,418 Red, Neutral188 0,248 0,429 Red, Neutral189 0,232 0,435 Red, Neutral190 0,275 0,373 Red, Neutral191 0,270 0,405 Red, Neutral192 0,259 0,421 Red, Neutral193 0,237 0,455 Red, Neutral194 0,226 0,458 Red, Neutral195 0,218 0,462 Red, Neutral196 0,216 0,465 Red, Neutral197 0,211 0,465 Red, Neutral198 0,267 0,437 Red, Neutral199 0,252 0,450 Red, Neutral200 0,239 0,453 Red, Neutral201 0,232 0,459 Red, Neutral202 0,222 0,462 Red, Neutral203 0,274 0,422 Red, Neutral204 0,272 0,444 Red, Neutral205 0,258 0,447 Red, Neutral206 0,250 0,455 Red, Neutral207 0,291 0,432 Red, Neutral208 0,276 0,441 Red, Neutral209 0,264 0,452 Red, Neutral210 0,307 0,424 Red, Neutral211 0,293 0,438 Red, Neutral212 0,305 0,436 Red, Neutral213 0,264 0,456 Red, Neutral214 0,255 0,464 Red, Neutral215 0,247 0,467 Red, Neutral216 0,237 0,469 Red, Neutral217 0,227 0,468 Red, Neutral218 0,295 0,446 Red, Neutral219 0,288 0,463 Red, Neutral220 0,279 0,467 Red, Neutral221 0,262 0,469 Neutral222 0,311 0,459 Neutral223 0,295 0,464 Neutral224 0,288 0,470 Neutral225 0,331 0,448 Neutral226 0,318 0,464 Neutral

APPENDIX A 132

400 500 600 700

0

400

800

1200

wavelength [nm]

power

Figure A1: Daylight basis functions from which experimental illuminants weremodelled.

400 500 600 7000.000

0.002

0.004

0.006

0.008

wavelength [nm]

power

Figure A2: Monitor basis functions as provided by Delahunt & Brainard (2004a).These basis functions were used to model experimental illuminants which liedoutside of the daylight model.

APPENDIX A 133

400 500 600 700-0.4

-0.2

0.0

0.2

0.4

wavelength [nm]

power

Figure A3: Reflectance basis functions derived by Kelly et al. (1943). Thesebasis functions were used to model experimental surfaces.

Acknowledgments

I am grateful to

Karl–Heinz Bauml for his professional and kind mentoring. His analytical

and straightforward thinking was always of great help.

David Brainard for providing his experimental illuminants and monitor

basis functions.

Brian Wandell and Jeffrey DiCarlo for providing their large set of daylight

measurements.

Alp Aslan, Simon Hanslmayr, Bernhard Pastotter, Anuscheh Samenieh,

Tobias Staudigl, Christof Kuhbandner, Bernhard Spitzer, and Maria Wimber

for useful comments and for being such great collegues.

my wife Silvia for being always by my side. This thesis is dedicated to

her.

134

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